5. Tangent Planes and Chain Rule

Total Differential — Quiz

Test your understanding of total differential with 5 practice questions.

Practice Questions

Question 1

For a differentiable function $z=f(x,y)$, which expression gives the total differential $dz$?

Question 2

Let $f(x,y)=x^2y+3y$. What is the total differential $df$ at $(1,2)$ when $dx=0.1$ and $dy=-0.2$?

Question 3

What does the total differential of a differentiable function approximate near a point?

Question 4

Let $f(x,y)=\sqrt{x+y}$. Find $df$ at $(4,5)$ when $dx=1$ and $dy=0$.

Question 5

For $f(x,y,z)=xy+z^2$, which expression is the total differential $df$?