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

Calculating Higher-order Derivatives — Quiz

Test your understanding of calculating higher-order derivatives with 5 practice questions.

Practice Questions

Question 1

If $y=x^3-4x$, what is the second derivative $y''$?

Question 2

If $f(x)=\sin x$, what is $f''(x)$?

Question 3

A function has first derivative $f'(x)=5x^4-2x$. What is $f''(x)$?

Question 4

If $y=(3x^2+1)^5$, which derivative uses the chain rule and gives the first derivative?

Question 5

For the implicit equation $x^2+y^2=25$, what is $\frac{dy}{dx}$ at a general point $(x,y)$?