10. Topic 10(COLON) Multivariable and Statistical Mathematics

Lesson 10.1: Functions Of Several Variables And Partial Differentiation — Quiz

Test your understanding of lesson 10.1: functions of several variables and partial differentiation with 5 practice questions.

Practice Questions

Question 1

What is the first partial derivative of the function $f(x, y) = 3x^2y + 4y^2$ with respect to $x$?

Question 2

What is the second partial derivative of the function $g(x, y) = x^2y + xy^2$ with respect to $y$?

Question 3

For the function $h(x, y) = 5x^3 - 4xy + 2y^3$, what is $\frac{\partial h}{\partial y}$?

Question 4

What is the first partial derivative of $k(x, y) = e^{xy}$ with respect to $x$?

Question 5

If $f(x, y) = x^2 + y^2$, what is the second partial derivative $\frac{\partial^2 f}{\partial x^2}$?