Chain Rule Step 4
Practice Worksheet with Answers 1


If you have no problem identifying which function is inner and which is outer, the chain rule is probably as easy as walking in a rose garden - no stress ;) Okay, enough with analogies. Practice your skills with the following 22 examples and check the answers afterward.




Easy&Medium difficulty level examples from marathon, let's run!

Find the derivative of the given functions using the chain rule, check the solutions afterward:

Example 1

$f(x) = (2x + 1)^2$
Example 2

$f(x)=(5x-7)^6$
Example 3

$f(x)=e^{5x}$
Example 4

$f(x)=\frac{1}{2}e^{2x}$
Example 5

$ f(x)=cos(2x)$
Example 6

$f(x)=cos(sin(x))$
Example 7

$ f(x)=sin(x^2)$
Example 8

$f(x) = \tan(4x)$
Example 9

$ f(x) = \ln(3x + 1)$
Example 10

$ f(x)=\sqrt{x}$
Example 11

$ f(x)=\sqrt{3x^2+3}$
Example 12

$ f(x)=(3x^2+2x)^3$
Example 13

$ f(x)=\sqrt{4x^2+1}$
Example 14

$ f(x)=e^{2x^3+5x}$
Example 15

$ f(x)=sin(4x^2+1)^2$
Example 16

$ f(x)=tan(3x^2-5x)$
Example 17

$ f(x)=cotan(e^x+x^2)$
Example 18

$ f(x)=ln\Big(\frac{1}{x}\Big)$
Example 19

$ f(x)=(2x-\frac{1}{2})^{-\frac{1}{2}}$
Example 20

$ f(x)=\sqrt{5x^2-2x+4}$
Example 21

$ f(x)=sin(2x^8+4x^2+3x)$
Example 22

$ 5^{4x+2}$ :) check the rules

The next step is harder examples on differentiation of composite functions with 2 and more inner functions.