Free Printable Differentiation

1.

Find the derivative of:
f(x) = 7(3x+ 4)⁵

a)

35(3x + 4)⁵

b)

35(3x + 4)⁴

c)

105(3x + 4)⁵

d)

105(3x + 4)⁴

2.

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

a)

Power rule

b)

Product rule

c)

Quotient rule

d)

General Power Rule

3.

What is the derivative of f?

a)

1/(x - 1)^-1

b)

-1/(x - 1)^-2

c)

-1/(x - 1)

d)

-1/(x - 1)²

4.

What is the derivative of y = 2π?

a)

0

b)

2

c)

-2

d)

None of the above

5.

Derivative means the same thing as

a)

slope of the tangent line

b)

slope of the normal line

c)

exponent

d)

potato

6.

Calculate the gradient of f(x)=ln(x)+x at x=2/3

a)

0.261

b)

2.5

c)

1.5

d)

-0.405

7.

When do you use the chain rule?

a)

anytime you want

b)

when there is a function in a function

c)

where there are multiple layers to a lasagna (yum)

d)

when there is division

8.

How much do you love mathematics ?

a)

suka sangat2

b)

mathematics? Yang ada nombor tu kan

c)

#siscuba

d)

biasa2 je

9.

What rule best apply to find the derivative of y=x lnx

a)

product rule

b)

quotient rule

c)

power rule

d)

sum rule

10.

Find the derivative:
y=5x²e^3x

a)

y'=10xe^3x(2x+3)

b)

y'=5xe^3x(3x+2)

c)

y'=10ex^3x(3x+2)

d)

y'=5xe^3x(2x+3)

11.

a)

3x²

b)

x³

c)

6x

d)

3x² + x³

12.

Find dy/dx by Implicit Differentiation
x + 4y = 1

a)

-1/4

b)

-1

c)

4

d)

1

13.

If

y=x^x\ then\ find\ \frac{\text{d}y}{\text{d}x}

a)

$x^x\left(1+\ln x\right)$

b)

$x^x\left(\ln x\right)$

c)

$x.x^{x-1}$

d)

$\left(1+\ln x\right)$

14.

Find the derivative of $y=\log_9x$

a)

\frac{1}{\left(\log x\right)9}

b)

$\frac{\ln9}{x}$

c)

$\frac{1}{x\ln x}$

d)

$\frac{1}{\left(\ln9\right)x}$

15.

$\frac{\text{d}}{\text{d}y}\left(x^3-2xe^x\right)$

a)

$3x^2-2e^x\left(x+1\right)$

b)

$3x^2-2\left(e^x+\frac{x}{e^x}\right)$

c)

$3x^2-2xe^x\left(2x+1\right)$

d)

$3x^2-2x\left(2xe^x+\frac{1}{e^x}\right)$

16.

$\frac{\text{d}}{\text{d}y}\left(e^{\left(2x+1\right)}\right)^2$

a)

$4e^{\left(4x+2\right)}$

b)

$\frac{4}{e^{\left(4x+2\right)}}$

c)

$e^{\left(4x+2\right)}\left(8x^2+2x\right)$

d)

$\frac{\left(8x^2+2x\right)}{e^{\left(4x+2\right)}}$

17.

$\frac{\text{d}}{\text{d}y}\left(e^x+2x\right)^3$

a)

$3\left(e^x+2\right)\left(e^x+2x\right)^2$

b)

$3\left(e^x+2\right)^2$

c)

$3\left(e^x+4x^2\right)\left(e^x+2x\right)^2$

d)

$4\left(e^x+2\right)^4$

18.

a)

a

b)

b

c)

c

d)

d

Differentiation

Total questions: 18

Worksheet time: 1hrs 3mins

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