In this section, you'll find a set of exercises on derivatives, designed to help you strengthen the knowledge you've just gained. Each exercise comes with a full solution, detailing all the steps required to reach the correct answer. The aim of these exercises is to give you the chance to apply what you've learned and assess your understanding of the topics covered.

Here are the exercises you’ll encounter in the following pages:

  • Exercise 1: y=\sqrt[3]{x}\log_3(x)

  • Exercise 2: y=\ln\ln x

  • Exercise 3: y=\sqrt{2^x+\sqrt{x}}

  • Exercise 4: y=x^2(x^4-1)^3

  • Exercise 5: y=\displaystyle\frac{e^{-x^2}}{2-x}

  • Exercise 6: y=(x-1)e^{-\frac{1}{x}}

  • Exercise 7: y=4^{\sin^5(x)-3}

  • Exercise 8: y=\frac{1}{\ln(\cos(x))}

  • Exercise 9: y=\arcsin(\sqrt{x})+\arctan(x^2)

  • Exercise 10: y=(\sin x)^{\cos x}

  • Exercise 11: y=|x^2-2x-3|

Try to complete the exercises on your own before looking at the solutions. This will help you pinpoint any areas where you might need more explanation or additional practice.

Remember, these exercises won’t affect your final grade in the course; they are just a tool to help you strengthen your skills and practice at your own pace, without any pressure.

We recommend keeping the table of derivatives of elementary functions that we saw in the previous week handy.

Function f(x) Derivative f'(x)
Constant c 0
x^r r \cdot x^{r-1} \forall r \in \mathbb{R}
e^x e^x
\ln(x) \frac{1}{x}
a^x a^x \ln(a) \forall a > 0
\log_a(x) \frac{1}{x \ln(a)} \forall a > 0, a \ne 0
\sin(x) \cos(x)
\cos(x) -\sin(x)
\tan(x) \frac{1}{\cos^2(x)}
\arcsin(x) \frac{1}{\sqrt{1-x^2}}
\arccos(x) -\frac{1}{\sqrt{1-x^2}}
\arctan(x) \frac{1}{1+x^2}
\sinh(x) \cosh(x)
\cosh(x) \sinh(x)


 Download the Table

You can find a downloadable version of all the completed exercises in the Downloadable Documents section.

Happy practicing!