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