Free Printable Derivatives

1.

Find the derivative of
$f\left(x\right)=-\frac{2}{3}x^3-\frac{1}{2}x^2+9x$

a)

$-2x^2-x+9$

b)

$-2x^3-x^2+9x$

c)

$-\frac{2}{12}x^4-\frac{1}{6}x^3+\frac{9}{\ 2}x^2$

d)

$-2x^4-x^3+9x^2$

2.

Find the second derivative of the function $f\left(x\right)=2x-5x^6$

a)

$2-30x^5$

b)

$x^2-\frac{5}{7}x^7$

c)

$-30x^5$

d)

$-150x^4$

3.

Which of the following is the derivative of $y=\left(3x^4-7\right)\left(5x^2+1\right)$

a)

$\left(12x^3\right)\left(10x\right)$

b)

$\left(3x^4-7\right)\left(10x\right)+\left(12x^3\right)\left(5x^2+1\right)$

c)

$\left(3x^4-7\right)\left(10x\right)-\left(12x^3\right)\left(5x^2+1\right)$

d)

$\frac{3x^4-7}{10x}+\frac{12x^3}{5x^2+1}$

4.

Find the derivative of
$f\left(x\right)=x^4\sin\left(x\right)$

a)

$x^4\cos\left(x\right)-4x^3\sin\left(x\right)$

b)

$x^4\cos\left(x\right)+4x^3\sin\left(x\right)$

c)

$4x^3\cos\left(x\right)$

d)

$-4x^3\cos\left(x\right)$

5.

$\frac{d}{dx}\left[\sin\left(x^3-2x\right)\right]=$

a)

$\left(3x^2-2\right)\cos\left(x^3-2x\right)$

b)

$-\left(3x^2-2\right)\cos\left(x^3-2x\right)$

c)

$\cos\left(3x^2-2\right)$

d)

$\sin\left(3x^2-2\right)$

6.

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

a)

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

b)

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

c)

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

d)

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

7.

Find the derivative of $y=\sqrt{\ln x}$

a)

$y'=\frac{1}{2}\ln x$

b)

$y'=\frac{1}{2x\sqrt{\ln x}}$

c)

$y'=\frac{1}{2x}$

d)

$y'=\sqrt{\ln x}$

8.

Find the derivative f(x) = x²/e^x

a)

f'(x) = (x²e^x - 2xe^x) / (e^x)²

b)

f'(x) = (2xe^x + x²e^x) / (e^x)²

c)

f'(x) = (2xe^x - x²e^x) / (e^x)²

d)

f'(x) = x²e^x + 2xe^x

9.

Find dy/dx
xy+y²=2

a)

-y/(x+2y)

b)

y/(x+2y)

c)

-3y/x

d)

-3x/y

10.

Find dy/dx at a given point.

a)

5/4

b)

4/5

c)

1

d)

-5

11.

When does a curve have a horizontal tangent line?

a)

When x = 0

b)

When y = 0

c)

When $\frac{\text{d}y}{\text{d}x}=0$

d)

When $\frac{\text{d}y}{\text{d}x}is\ undefined$

12.

What best describes the value of the derivative at x =3?

a)

Positive

b)

Negative

c)

Zero

d)

Not Differentiable

13.

At which point(s) will the slopes of the tangent line are zero?

a)

at C only

b)

at points A, C and E only

c)

at point B and D only

d)

at points A and E only

14.

What is the equation of the line tangent to the curve y = -x² + 3 at (1, 2)?

a)

y = 2x - 4

b)

y = -2x - 4

c)

y = -2x + 4

d)

y = 2x + 4

15.

What is the rate of change of f(t) = 2t³ - 4t + 1 when t = 2s and f is in meter (m)?

a)

16 m/s

b)

20 m/s

c)

24 m/s

d)

30 m/s

16.

The radius of a sphere is decreasing at a rate of 2 cm/sec. At the instant when the radius of the sphere is 3 cm, what is the rate of change, in cm²/sec, of the surface area of the sphere? (The surface area of a sphere is A = 4πr².)

a)

-108π

b)

-72π

c)

-48π

d)

-24π

17.

For what values of x will f'(x)=0?

a)

-3, -1, 0, 3

b)

-3, -1, 0

c)

-1, 0

d)

-3

Derivatives - all

Total questions: 17

Worksheet time: 3570secs

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