3. Partial Derivatives

Partial Derivatives — Quiz

Test your understanding of partial derivatives with 5 practice questions.

Practice Questions

Question 1

Find the first-order partial derivative of the function $f(x,y) = x^2 y + 3xy^3$ with respect to $x$.

Question 2

Compute the second-order mixed partial derivative $\frac{\partial^2 f}{\partial x \partial y}$ for the function $f(x,y) = \sin(xy) + x^2 y$.

Question 3

If $f(x,y) = e^{x^2 y}$, what is $\frac{\partial f}{\partial y}$?

Question 4

Consider the function $f(x,y) = x^3 + 3x^2 y - y^3$. Find all the critical points by solving $\frac{\partial f}{\partial x} = 0$ and $\frac{\partial f}{\partial y} = 0$.

Question 5

Find the partial derivative $\frac{\partial f}{\partial x}$ for $f(x,y) = \ln(x^2 + y^2)$.