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.