# Worksheet: The Chain Rule for Multivariate Functions

In this worksheet, we will practice using the chain rule with partial derivative of multivariable functions, such as finding ∂ f(x,y) / ∂u, where x=g(u,v) and y=h(u,v).

**Q1: **

Let over the curve , . Write an expression for , giving your answer in terms of the partial derivatives of .

- A
- B
- C
- D
- E

**Q2: **

The differentiable functions , describe a curve with . Use the chain rule to find an expression for , where .

- A
- B
- C
- D
- E

**Q3: **

Let and consider the curve given by . Use the chain rule to determine the values of when . You may keep your answer in terms of .

- A where is an integer
- B where is an integer
- C where is an integer
- D where is an integer
- E where is an integer

**Q4: **

Let over the curve , , . Write an expression for , giving your answer in terms of the partial derivatives of .

- A
- B
- C
- D
- E

**Q5: **

The function can be considered in terms of the polar coordinates via the transformation where and . By considering as the second component of , or otherwise, write an expression for this partial derivative in terms of and .

- A
- B
- C
- D
- E