2. Derivatives

Implicit Differentiation — Quiz

Test your understanding of implicit differentiation with 5 practice questions.

Practice Questions

Question 1

When differentiating an equation implicitly, what is the key difference when differentiating a term involving $y$ compared to a term involving $x$?

Question 2

Given the equation $x^2 + y^2 = 16$, what is the result of differentiating both sides with respect to $x$?

Question 3

After differentiating an equation implicitly and collecting all terms with $\frac{dy}{dx}$ on one side, what is the final step to solve for $\frac{dy}{dx}$?

Question 4

For the equation $x^2 + y^2 = 5$, what is the value of $\frac{dy}{dx}$ at the point $(1, 2)$?

Question 5

Which of the following is an example of a relation where implicit differentiation would be necessary to find $\frac{dy}{dx}$?