3. Partial Derivatives

Chain Rule And Implicit Differentiation — Quiz

Test your understanding of chain rule and implicit differentiation with 5 practice questions.

Practice Questions

Question 1

If $z = (x^2 + y^2)^3$, and $x = t^2$, $y = t^3$, what is $\frac{dz}{dt}$ using the chain rule?

Question 2

Find $\frac{\partial z}{\partial x}$ if $z = \sin(xy)$.

Question 3

If $z = e^{x^2 + y^2}$ and $x = 2t$, $y = 3t$, what is $\frac{dz}{dt}$?

Question 4

Find $\frac{\partial z}{\partial y}$ if $z = x^3 + 2xy + y^2$.

Question 5

If $w = x^2y^3$, and $x = t^2$, $y = t^3$, what is $\frac{dw}{dt}$?