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

Selecting Procedures For Calculating Derivatives — Quiz

Test your understanding of selecting procedures for calculating derivatives with 5 practice questions.

Practice Questions

Question 1

Which procedure is most suitable for differentiating $y=\ln(5x^2+4)$?

Question 2

If $y=\sqrt{1+(x^2+1)^3}$, what is $\frac{dy}{dx}$?

Question 3

For the curve defined by $x^2+y^2=25$, what is $\frac{dy}{dx}$ at the point $(3,4)$?

Question 4

If $f(x)=\arcsin(2x^2-1)$, what is $f'(\tfrac{1}{2})$?

Question 5

Suppose $f(1)=4$ and $f'(1)=\tfrac{1}{2}$. If $h(x)=f^{-1}(x^2)$, what is $h'(2)$?