3. Partial Derivatives

Partial Derivatives — Quiz

Test your understanding of partial derivatives with 5 practice questions.

Practice Questions

Question 1

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

Question 2

For the function $g(x,y) = e^{x^2y}$, what is the partial derivative of $g$ with respect to $y$?

Question 3

Consider $f(x,y) = \sin(xy)$. What is the partial derivative of $f$ with respect to $x$?

Question 4

If $h(x,y) = x^3 + 4x^2y^2 + y^4$, what is the partial derivative of $h$ with respect to $y$?

Question 5

Find the second-order partial derivative $\frac{\partial^2 f}{\partial x^2}$ for $f(x,y) = x^4y + 2x^2y^3$.