Differentiation Bridge Course

Multiple Choice

Find the derivative of f(x) = 6x³⁰ -2x¹⁵ + 4x³ - 2x + 1

• f'(x) = 18x²⁹ + 30x¹⁵ + 12x³ 

• f'(x) = 180x²⁹ - 30x¹⁴ + 12x² 

• f'(x) = 180x²⁹ - 30x¹⁴ + 12x² - 2

• f'(x) = 180x²⁹ - 30x¹⁴ + 12x² +1

Multiple Choice

FInd the derivative:

f(x) = (-2/3)x³ - (1/2)x² + 9x

• -2x² - x + 9

• -2x² + x + 9

• 2x² - x + 9

• 2x² - x - 9

Multiple Choice

Multiple Choice

$$\frac{\text{d}x}{\text{d}y}\sin\left(x\right)$$  

• cos(x)

• -cos(x)

• -cot(x)

• cot(x)

Multiple Choice

• cosx

• -cosx

• -sinx cosx

• sinx cosx

Multiple Choice

FInd the derivative:
f(x) = (-2/3)x³ - (1/2)x² + 9x

• -2x² - x + 9

• -2x² + x + 9

• 2x² - x + 9

• 2x² - x - 9

Multiple Choice

Find the derivative. f(x) = 1/(3x²) + 4x³

• f'(x) = 6x³ + 12x²
• f'(x) = 6x + 12x²
• f'(x) =  -2/(3x³) + 12x²
• f'(x) = -6/x² + 12x²

Multiple Choice

Set up the derivative of y=(3x⁴ - 7)*(5x² + 1)

• (12x³)*(10x)
• (3x⁴ - 7)*(10x) + (12x³)*(5x² + 1)
• (3x⁴ - 7)*(10x) - (12x³)*(5x² + 1)
• (3x⁴ - 7)/(10x) + (12x³)/(5x² + 1)

Multiple Choice

• sinx
• -sinx
• -cscx cotx
• sec²x

Multiple Choice

Differentiate f(x) =(2/ x⁵) - 5.

• x⁵-3
• -10x⁶ 
• x⁵-5
• -10x^-6 

Multiple Choice

$$\frac{\text{d}x}{\text{d}y}\text{cos(x)}$$  

• sec(x)

• sin(x)

• -sin(x)

• -sec(x)

Multiple Choice

Find the derivative.

• x⁴ cosx - 4x³sinx
• x⁴ cosx + 4x³sinx
• 4x³cosx
• -4x³cosx

Multiple Choice

• cscx cotx
• secx tanx
• sec²x
• -cscx cotx

Multiple Choice

Find the derivative f(x) = xe^x

• f'(x) = e^x

• f'(x) = xe^x + xe^x

• f'(x) = e^x - xe^x

• f'(x) = e^x + xe^x

Multiple Choice

Find: f'(x) =

• 9x^-1/3

• -3x^-4/3

• -9x^2/3

• -3x^2/3

Multiple Choice

.

• (3x²-2)cos(x³-2x)

• -(3x²-2)cos(x³-2x)

• cos(2x²-2)

• sin(2x²-2)

Multiple Choice

• secx tanx
• sec²x
• cscx cotx
• -cscx cotx

Multiple Choice

Find the derivative of g(x)=(3x-2)/(x²+2)

• 9x²+2
• 3(x²+2)/(x²+2)²
• (-3x²+4x +6)/(x²+2)²
• (-3x²+10)/(x²+2)²

Multiple Choice

tan(x)

• sin(x)

• $$\sec^2\left(x\right)$$

• -sec(x)

• $$\sin^2\left(x\right)$$

Multiple Choice

Find the derivative
f(t) = (t² + 2t)⁵

• f'(t) = 5(2t+2)⁴
• f'(t) = 5(t² + 2t)⁴
•  f'(t) = 5(t² + 2t)⁴(2t)
• f'(t) = 5(t² + 2t)⁴(2t + 2)

Multiple Choice

• secx tanx
• -secx tanx
• tan²x
• cscx cotx

Multiple Choice

Find the derivative.
f(x) = -8x^-3 + 5x - e^x

• f'(x) = -24x^-4 + 5 - e^x
• f'(x) = 24x^-4 + 5 - e^x
• f'(x) = 24x^-2 + 5 - e^x
• f'(x) = 24x^-4 + 5 - e^x-1

Multiple Choice

Find the second derivative of the function:
f (x) =  2x - 5x⁶

• f ''(x)= 2 - 30x
• f ''(x) =  2-30x⁵
• f ''(x) = -30x⁵
• f ''(x) = -150x⁴

Multiple Choice

f(x)= 9/∛x
f'(x) =

• 9x^-1/3
• -3x^-4/3
• -9x^2/3
• -3x^2/3

Multiple Choice

• -cscx cotx
• cscx cotx
• -csc²x
• csc²x

Multiple Choice

Find the second derivative of
f(x) = x² + e^x  - cosx

• f"(x) = 2 + e^x + cosx
• f"(x) = 2x + e^x + cosx
• f"(x) = 2x + xe^x - cosx
• f"(x) = 2x + e^x + sinx

Multiple Choice

sec(x)

• cos(x)tan(x)

• sec(x)tan(x)

• sin(x)cos(x)

• sin(x)tan(x)

Multiple Choice

Find y' if y=e^3x

• e^3x
• e^2x
• 0
• 3e^3x

Multiple Choice

d/dx (sin³(4x^-6)) = ?

• -24x^-5 ⋅ cos (4x^-6) ⋅ 3sin²(4x^-6)
• -24x^-7 ⋅ cos (4x^-6) ⋅ 3sin²(4x^-6)
• -24x^-7 ⋅ 3cos²(4x^-6)
• 3cos²(-24x^-5)

Multiple Choice

Let y = (x - 1)(x + 2). Find dy/dx.

• 2x + 1

• 2x - 1

• 4x - 1

• 2x² + x - 1

Multiple Choice

Find $$\frac{d^2y^{ }}{dx^2}$$  by Implicit Differentiation 
$$x^3+y^3=36$$  

• $$\frac{-x^2}{y^2}$$  

• $$\frac{-2xy^2+2xy}{y^2}$$  

• $$\frac{-2xy^3-2x^4}{y^5}$$  

• $$\frac{-2xy^2-2x^4}{y^4}$$  

Multiple Choice

Choose the best rule to derive the function.

• Product rule

• Quotient rule

• Power rule

• Chain rule

Multiple Choice

Find the derivative.

• x⁴ cosx - 4x³sinx
• x⁴ cosx + 4x³sinx
• 4x³cosx
• -4x³cosx

Multiple Choice

What rule should be used in deriving h(x) = 2(x - 4)³

• Power rule

• Product rule

• Quotient rule

• Chain rule

Multiple Choice

cot(x)

• $$-\cos^2\left(x\right)$$
  

• $$-\csc^2\left(x\right)$$

• $$\cos\left(x\right)\cot\left(x\right)$$

• sec(x)tan(x)

Multiple Choice

What is the derivative of xⁿ?

• (n-1)xⁿ
• nxⁿ⁺¹
• (n+1)x^n-1
• nx^n-1

Multiple Choice

What is f'(x) if f(x) = cos(5x⁴)?

• f'(x) = sin(20x³)
• f'(x) = 20x³ sin(5x⁴)
• f'(x) = -sin(20x³)
• f'(x) = -20x³ sin(5x⁴)

Multiple Choice

Find the derivative.

• x⁴ cosx - 4x³sinx
• x⁴ cosx + 4x³sinx
• 4x³cosx
• -4x³cosx

Multiple Choice

Find the derivative f(x) = (3x + 5)⁴

• f'(x) = 12(3x)³
• f'(x) = 12(3x + 5)³
• f'(x) = (3)⁴
• f'(x) = (3x + 5)³

Multiple Choice

What is f'(x) if f(x) = cos(5x⁴)?

• f'(x) = sin(20x³)
• f'(x) = 20x³ sin(5x⁴)
• f'(x) = -sin(20x³)
• f'(x) = -20x³ sin(5x⁴)

Multiple Choice

Find dy/dx if y = cos⁵x

• 5cos⁴x
• -5sin⁴x
• 5cos⁴xsinx
• -5cos⁴xsinx

Multiple Choice

Find y' if y = tan(3x²+2).

• sec²(3x²+2)
• 6xsec²(3x²+2)
• 6xsec²x(3x²+2)
• sec²(6x)

Multiple Choice

csc(x)

• -csc(x)cot(x)

• sec(x)tan(x)

• $$-\csc^2\left(x\right)$$

• $$\sec^2\left(x\right)$$

Multiple Choice

Find dy/dx if y = (cscx + 1)⁷

• -7(cscx + 1)⁶(cscxcotx)
• 7(-cscxcotx)⁶
• 7(cscx + 1)⁶(cscxcotx)
• -7(cscxcotx)⁶

Multiple Choice

Find y' if y = tan(3x²+2).

• sec²(3x²+2)
• 6xsec²(3x²+2)
• 6xsec²x(3x²+2)
• sec²(6x)

Multiple Choice

Find the derivative f(x) = tanxcosx

• f'(x) = sec²xcosx - tanxsinx
• f'(x) = sec²xcosx + tanxsinx
• f'(x) = sec²xsinx
• f'(x) = sec²xcosx - tanxcosx

Multiple Choice

Find dy/dx by Implicit Differentiation

x + 4y = 1

• -1/4

• -1

• 4

• 1

Multiple Choice

Find the derivative of f(x) = x²sinx

• f'(x) = 2xsinx - x²cosx
• f'(x) = 2xsinx + x²sinx
• f'(x) = 2xsinx + x²cosx
• f'(x) = 2xcosx

Multiple Choice

Find dy/dx if y = sec(8x²).

• sec(16x)tan(16x)
• 16xcos(8x²)
• 16xsecxtanx(8x²)
• 16xsec(8x²)tan(8x²)

Multiple Choice

Find the derivative of    f(x) = (x^6 + 4)^5

• f '(x) = 5x^5(x^4 + 4)^4
• f '(x) = 6x^5(x^6 + 4)^4
• f '(x) = 30x^5(x^6 + 4)
• f '(x) = 30x^6(x^6 + 4)

Multiple Choice

$$\sin^{-1}\left(x\right)$$  

• $$\frac{1}{\sqrt{1-x^2}}$$  

• $$\frac{1}{\sqrt{1+x^2}}$$  

• $$-\frac{1}{\sqrt{1+x^2}}$$  

•   $$-\frac{1}{\sqrt{1-x^2}}$$   

Multiple Choice

Which of the following is the derivative of the function h(t) = t⁴ - (t⁴ - 1)⁸ ?

• h^'(t)= 4t³ - 8t³(t⁴ - 1)⁸

• h^'(t)= 4t³ - 32t³(t⁴ - 1)⁷

• h^'(t)= 4t³ - 8(t⁴ - 1)⁷

• h^'(t)= 4t² - 32t³(t⁴ - 1)⁸

Multiple Choice

Find g'(x) if g(x) = sin^1/2(4x)

• 2cos^-1/2(4x)
• 4cos^1/2(4x)
• 2sin^-1/2(4x)cos(4x)
• 1/2sin^-1/2(4x)cos(4x)

Multiple Choice

Differentiate y = $$\frac{12}{x^2}$$  

• y' = 24x^-1

• y' = -24x^-3

• y' = -24x^-1

• y' = 6x^-3

Multiple Choice

Set up the derivative of y=(3x⁴ - 7)*(5x² + 1)

• (12x³)*(10x)
• (3x⁴ - 7)*(10x) + (12x³)*(5x² + 1)
• (3x⁴ - 7)*(10x) - (12x³)*(5x² + 1)
• (3x⁴ - 7)/(10x) + (12x³)/(5x² + 1)

Multiple Choice

Find dy/dx if y = (cscx + 1)⁷

• -7(cscx + 1)⁶(cscxcotx)
• 7(-cscxcotx)⁶
• 7(cscx + 1)⁶(cscxcotx)
• -7(cscxcotx)⁶

Multiple Choice

$$\cos^{-1}\left(x\right)$$  

• $$\frac{1}{\sqrt{1+x^2}}$$  

• $$\frac{1}{\sqrt{1-x^2}}$$  

• $$-\frac{1}{\sqrt{1-x^2}}$$  

• $$-\frac{1}{\sqrt{1+x^2}}$$  

Multiple Choice

If f(x) = 4tan(x/2), then f'(x) =

• 4sec²(x/2)

• -4csc²(x/2)

• 2sec²(x/2)

• -2csc²(x/2)

Multiple Choice

• A

• B

• C

• D

Multiple Choice

.

• (3x²-2)cos(x³-2x)

• -(3x²-2)cos(x³-2x)

• cos(2x²-2)

• sin(2x²-2)

Multiple Choice

$$\tan^{-1}\left(x\right)$$  

• $$\frac{1}{1+x^2}$$  

• $$\frac{1}{1-x^2}$$  

• - $$\frac{1}{1-x^2}$$  

• $$-\frac{1}{1+x^2}$$  

Multiple Choice

Find the derivative f(x) = tanxcosx

• f'(x) = sec²xcosx - tanxsinx
• f'(x) = sec²xcosx + tanxsinx
• f'(x) = sec²xsinx
• f'(x) = sec²xcosx - tanxcosx

Multiple Choice

Find the derivative f(x) = xe^x

• f'(x) = e^x

• f'(x) = xe^x + xe^x

• f'(x) = e^x - xe^x

• f'(x) = e^x + xe^x

Multiple Choice

Find the derivative of f(x) = x²sinx

• f'(x) = 2xsinx - x²cosx
• f'(x) = 2xsinx + x²sinx
• f'(x) = 2xsinx + x²cosx
• f'(x) = 2xcosx

Multiple Choice

$$\cot^{-1}\left(x\right)$$  

• $$-\frac{1}{1+x^2}$$  

• $$-\frac{1}{1-x^2}$$  

• $$\frac{1}{1+x^2}$$  

• $$\frac{1}{1-x^2}$$  

Multiple Choice

Find y' if y = tan(3x²+2).

• sec²(3x²+2)

• 6xsec²(3x²+2)

• 6xsec²x(3x²+2)

• sec²(6x)

Multiple Choice

$$\sec^{-1}\left(x\right)$$  

• $$\frac{1}{\sqrt{x^2-1}}$$  

• $$\frac{1}{x\sqrt{x^2-1}}$$  

• $$-\frac{1}{x\sqrt{x^2-1}}$$  

• $$-\frac{1}{\sqrt{x^2-1}}$$  

Multiple Choice

Find the derivative of y = 2x² (3x - 4)

• 6x³ - 8x²
• 18x² - 16x
• 15x² - 6x
• 6x - 4

Multiple Choice

$$\csc^{-1}\left(x\right)$$  

• $$\frac{1}{x\sqrt{x^2-1}}$$  

• $$-\frac{1}{x\sqrt{x^2-1}}$$  

• $$\frac{1}{\sqrt{1-x^2}}$$  

• $$\frac{1}{x^2\sqrt{1-x}}$$  

Multiple Choice

Find the derivative:

y=log₉x

• y′=1 /((log9)x)

• y′=(ln9)/x

• y′=1/(x(lnx))

• y′=1/((ln9)x)

Multiple Choice

Find the derivative f(x) = x²/e^x

• f'(x) = (x²e^x - 2xe^x) / (e^x)²
• f'(x) = (2xe^x + x²e^x) / (e^x)²
• f'(x) = (2xe^x - x²e^x) / (e^x)²
• f'(x) = x²e^x + 2xe^x

Multiple Choice

Find the derivative:

y=(2^3x+4)

• 3(ln2)(2^3x+4)

• 3(2^3x+4)

• 3(2^3x+4/(ln2))

• 2^3x+4

Multiple Choice

Differentiate f(x) =(2/ x⁵) - 5.

• x⁵-3
• -10x⁶ 
• x⁵-5
• -10x^-6 

Multiple Choice

Find the derivative f(x) = xe^x

• f'(x) = e^x

• f'(x) = xe^x + xe^x

• f'(x) = e^x - xe^x

• f'(x) = e^x + xe^x

Multiple Choice

Find y' if y = tan(3x²+2).

• sec²(3x²+2)
• 6xsec²(3x²+2)
• 6xsec²x(3x²+2)
• sec²(6x)

Multiple Select

log(4x)

• log4-logx

• log4+logx

• 4logx

• xlog4

Multiple Choice

Find the derivative.

• x⁴ cosx - 4x³sinx
• x⁴ cosx + 4x³sinx
• 4x³cosx
• -4x³cosx

Multiple Choice

log(xy²)

• logx+2logy

• logx+logy²

• logx-2logy

• logx+logy+log2

Multiple Choice

Find g'(x) if g(x) = sin^1/2(4x)

• 2cos^-1/2(4x)
• 4cos^1/2(4x)
• 2sin^-1/2(4x)cos(4x)
• 1/2sin^-1/2(4x)cos(4x)

Multiple Choice

$$\log\left(\frac{x}{y}\right)$$  

• logx+logy

• xlogy

• log(x-y)

• logx-logy

Multiple Choice

Find the derivative f(x) = xe^x

• f'(x) = e^x

• f'(x) = xe^x + xe^x

• f'(x) = e^x - xe^x

• f'(x) = e^x + xe^x

Multiple Choice

Choose the best answer

• A

• B

• C

• D

Multiple Choice

Find y' if y = cos⁵(4x³)

• -5cos⁴(4x³)sin(12x²)
• -60x²sin⁴(4x³)
• -5cos⁴(4x³)sin(4x³)
• -60x²cos⁴(4x³)sin(4x³)

Multiple Choice

$$if\ y=\log\ \tan\left(\frac{\pi}{4}+\frac{x}{2}\right),\ then\ \frac{dy}{dx\ }\ =$$  

• $$\sec x$$  

• $$\operatorname{cosec}x$$  

• $$\sec\left(\frac{\pi}{4}+\frac{x}{2}\right)$$  

• $$\cos\left(\frac{\pi}{4}+\frac{x}{2}\right)$$  

Multiple Choice

.

• (3x²-2)cos(x³-2x)

• -(3x²-2)cos(x³-2x)

• cos(2x²-2)

• sin(2x²-2)

Multiple Choice

$$find\ the\ derivativeof\log\log\log x^3$$  

• $$\frac{1}{\left(x\log x\right)\left(\log\ \log\ x^3\right)}$$  

• $$\frac{1}{\left(\log x\right)\left(\log\ \log\ x^3\right)}$$  

• $$\frac{1}{\left(x\log x^3\right)\left(\log\ \log\ x^3\right)}$$  

• $$\frac{1}{\left(x^3\log x\right)\left(\log\ \log\ x^3\right)}$$  

Multiple Choice

Set up the derivative of y=(3x⁴ - 7)*(5x² + 1)

• (12x³)*(10x)
• (3x⁴ - 7)*(10x) + (12x³)*(5x² + 1)
• (3x⁴ - 7)*(10x) - (12x³)*(5x² + 1)
• (3x⁴ - 7)/(10x) + (12x³)/(5x² + 1)

Multiple Choice

$$differentiate\ \cos\left(\log x\ +\ e^x\right)$$  

• $$-\frac{1}{x}\sin\left(\log x\ +\ e^x\right)\left(1+xe^x\right)$$  

• $$\frac{1}{x}\sin\left(\log x\ +\ e^x\right)\left(1+xe^x\right)$$  

• $$-\frac{e^x}{x}\sin\left(\log x\ +\ e^x\right)\left(1+xe^x\right)$$  

• $$-\frac{1}{x}\cos\left(\log x\ +\ e^x\right)\left(1+xe^x\right)$$  

Multiple Choice

Find the derivative of g(x)=(3x-2)/(x²+2)

• 9x²+2
• 3(x²+2)/(x²+2)²
• (-3x²+4x +6)/(x²+2)²
• (-3x²+10)/(x²+2)²

Multiple Choice

$$Differentiate\ \frac{e^x}{\sin x}$$  

• $$\frac{e^x\left(\sin x-\cos x\right)}{\sin^2x}$$  

• $$\frac{e^x\left(\sin x+\cos x\right)}{\sin^2x}$$  

• $$\frac{e^x\left(\cos x\ -\sin x\right)}{\sin^2x}$$  

• $$\frac{e^x\left(\sin x-\cos x\right)}{\cos^2x}$$  

Multiple Choice

Find the second derivative of
f(x) = x² + e^x  - cosx

• f"(x) = 2 + e^x + cosx
• f"(x) = 2x + e^x + cosx
• f"(x) = 2x + xe^x - cosx
• f"(x) = 2x + e^x + sinx

Multiple Choice

Differentiate

$$\cos^{-1}\left(e^x\right)$$  

• $$-\frac{e^x}{\sqrt{1\ -e^{2x}}}$$  

• $$\frac{e^x}{\sqrt{1\ -e^{2x}}}$$  

• $$-\frac{e^x}{\sqrt{1\ -e^x}}$$  

• $$-\frac{e^x}{\sqrt{1\ +e^{2x}}}$$  

Multiple Choice

The position of an object is given as a function of time by x = 3t² + 5t³ - 2t
What is the acceleration of the object at time t = 2 s?

• 64 m/s/s
• 60 m/s/s
• 66 m/s/s
• 70 m/s/s

Multiple Choice

$$differentiate\ 5^{\sin x}$$  

• $$5^{\sin x}\cos x.\ \log5$$  

• $$5^{\sin x}\cos x.\ \log e$$  

• $$5^{\cos x}\cos x.\ \log5$$  

• None of these

Multiple Choice

Find the derivative of:

• a

• b

• c

• d

Multiple Choice

$$differentiate\ \tan^{-1}\left(\log x\right)$$  

• $$\frac{1}{x\left[1+\left(\log x\right)^2\right]}$$  

• $$\frac{x}{\left[1+\left(\log x\right)^2\right]}$$  

• $$\frac{\log x}{x\left[1+\left(\log x\right)^2\right]}$$  

• $$\frac{1}{x\left[1+\log x\right]}$$  

Multiple Choice

The velocity of an object is given as v = 2t + 3t³. what is the acceleration of the object at t = 2 s?

• 38 m/s/s
• 27 m/s/s
• 16 m/s/s
• 49 m/s/s

Multiple Choice

Find the derivative of 
$$f\left(x\right)=\ln\left(\cos\left(5x^2\right)\right)$$  

• $$\frac{1}{\cos\left(5x^2\right)}$$  
  

• $$-\frac{\left(10x\ \sin\left(5x^2\right)\right)}{\ \cos\left(5x^2\right)}$$  
  

• $$-\frac{1}{10x\sin\left(5x^2\right)}$$  
  

• $$\frac{-\sin\left(5x^2\right)}{\cos\left(5x_{ }^2\right)}$$  

Multiple Choice

If the position function for a particle is s(t) = -t² - t, what is the instantaneous velocity function for the particle? 

• v(t) = -2
• v(t) = -2t - 1 
• v(t) = t³
• v(t) = -t

Multiple Choice

Find the derivative:

y=log₉x

• y′=1 /((log9)x)

• y′=(ln9)/x

• y′=1/(x(lnx))

• y′=1/((ln9)x)

Multiple Choice

If the position of a particle is represented by x(t) = -t² + 1, what is its instantaneous velocity at t = 1?  

• v = 0
• v = 1
• v = -1
• v = -2

Multiple Choice

Which if the following is not a correct notation for 'derivative?'

• f'(x)
• y'
• dy
• dy/dx

Multiple Choice

Find the derivative.
f(x) = -8x^-3 + 5x - e^x

• f'(x) = -24x^-4 + 5 - e^x
• f'(x) = 24x^-4 + 5 - e^x
• f'(x) = 24x^-2 + 5 - e^x
• f'(x) = 24x^-4 + 5 - e^x-1

Multiple Choice

• A

• B

• C

• D

Multiple Choice

Find the derivative
f(t) = (t² + 2t)⁵

• f'(t) = 5(2t+2)⁴
• f'(t) = 5(t² + 2t)⁴
•  f'(t) = 5(t² + 2t)⁴(2t)
• f'(t) = 5(t² + 2t)⁴(2t + 2)

Multiple Choice

How many derivatives can you take of a function?

• only 3
• only 2
• only 1
• until you can no longer derive it

Multiple Choice

Find the second derivative of
f(x) = x² + e^x  - cosx

• f"(x) = 2 + e^x + cosx
• f"(x) = 2x + e^x + cosx
• f"(x) = 2x + xe^x - cosx
• f"(x) = 2x + e^x + sinx

Multiple Choice

Which of the following is the quotient rule for derivatives?

• h^'(x)=((g(x)f^'(x) + f(x)g^'(x)) / (g(x))²

• h^'(x)=((g^'(x)f^'(x) - f(x)g(x)) / (g(x))

• h^'(x)=((g(x)f^'(x) - f(x)g^'(x)) / (g(x))²

• h^'(x)=((g^'(x)f^'(x) + f(x)g(x)) / (g(x))

Multiple Choice

f(x)= 9/∛x
f'(x) =

• 9x^-1/3
• -3x^-4/3
• -9x^2/3
• -3x^2/3

Multiple Choice

Which of the following is the chain rule for derivatives utilizing the original function h(x) = f(g(x))

• h^'(x)=(f^'(g(x))(f^'(x))

• h^'(x)=(f^'(g(x))(g(x))

• h^'(x)=(f^'(g(x))(f(x))

• h^'(x)=(f^'(g(x))(g^'(x))

Multiple Choice

f(x)= 9/∛x
f'(x) =

• 9x^-1/3
• -3x^-4/3
• -9x^2/3
• -3x^2/3

Multiple Choice

Find dy/dx by Implicit Differentiation
xy = 6

• -x/ y
• -y/ x
• -6y/ x
• y/x

Multiple Choice

Find y' if y=e^3x

• e^3x
• e^2x
• 0
• 3e^3x

Multiple Choice

The acceleration function is the first derivative of...

• position

• velocity

• calculus

• particle motion

Multiple Choice

$$derive\ y=\sin\left(5x\right)\ with\ respect\ to\ x$$  

• $$-\cos\left(5x\right)$$  

• $$\cos\left(5x\right)$$  

• $$5\cos\left(5x\right)$$  

• $$\sec\left(5x\right)$$