Multi-Variable Chain Rule

Practice Questions

Calculus 3 › Multi-Variable Chain Rule

Page 1 of 4

10 of 34

1

Find $\frac{dz}{dt}$ if , and .

2

Find $\frac{\mathrm{dh} }{\mathrm{d} t}$ , where and , $y=e^{t^2}$

3

Compute $\frac{dz}{dt}$ for $z=2xe^{xy}$ , , $y=t^{-2}$ .

4

Find $\frac{dz}{dt}$ if $z=e^{x+y}$ , and .

5

Use the chain rule to find $\frac{dr}{dt}$ when , , .

6

Find $\frac{dz}{dt}$ if , and .

7

Find $\frac{dz}{dt}$ if , and .

8

Use the chain rule to find $\frac{dr}{dt}$ when , , .

9

Use the chain rule to find $\frac{dr}{dt}$ when $r=\frac{4x^2+8y^2}{x^3}$ , , .

10

Use the chain rule to find $\frac{dr}{dt}$ when $r=e^{x+y}$ , , .

Page 1 of 4

Return to subject