3. Partial Derivatives

Directional Derivatives And Gradient — Quiz

Test your understanding of directional derivatives and gradient with 5 practice questions.

Practice Questions

Question 1

What is the definition of the directional derivative of a function $f(x, y)$ at a point in the direction of a vector $\mathbf{u}$?

Question 2

Which of the following represents the gradient vector $\nabla f$ of the function $f(x, y)$?

Question 3

What is the directional derivative of $f(x, y) = x^2 + y^2$ at the point $(1, 1)$ in the direction of the vector $\mathbf{u} = \left( \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}} \right)$?

Question 4

In which direction does the gradient vector point at a given point for a function $f(x, y)$?

Question 5

What is the magnitude of the gradient vector $\nabla f(x, y)$ for $f(x, y) = 3x^2 + 4y^2$ at the point $(2, -1)$?