2. Pure Calculus

Differentiation — Quiz

Test your understanding of differentiation with 5 practice questions.

Practice Questions

Question 1

Given $y = x^2 e^{3x} \sin(2x)$, find $\frac{dy}{dx}$.

Question 2

A student defines $y=\frac{\ln(x^2+1)}{x^3}$. What is $\frac{dy}{dx}$?

Question 3

For the parametric curve $x=\ln t$, $y=t^2+\frac{1}{t}$, find $\frac{d^2y}{dx^2}$ at $t=1$.

Question 4

If $y=\arctan(x^2)$, what is $\frac{d^2y}{dx^2}$?

Question 5

Using logarithmic differentiation, find $\frac{dy}{dx}$ for $y=x^{x^2}$.