3. Differentiation(COLON) Composite, Implicit, and Inverse Functions

The Chain Rule — Quiz

Test your understanding of the chain rule with 5 practice questions.

Practice Questions

Question 1

What does the chain rule say for a composite function $y=f(g(x))$?

Question 2

If $y=(3x+2)^5$, what is $\dfrac{dy}{dx}$?

Question 3

If $y=\sin(x^2)$, what is $\dfrac{dy}{dx}$?

Question 4

If $y=\sqrt{1-x^3}$, what is $\dfrac{dy}{dx}$?

Question 5

Suppose $y=f(g(x))$, $f'(2)=4$, and $g'(1)=3$. If $g(1)=2$, what is $\dfrac{dy}{dx}$ when $x=1$?