- #1

mopit_011

- 17

- 8

- Homework Statement
- N/A

- Relevant Equations
- N/A

In Chapter 3 of Thomas’s Calculus, they give the following proof of the Chain Rule. After the proof, the text says that this proof doesn’t apply when the function g(x) oscillates rapidly near the origin and therefore leads delta u to be 0 even when delta x is not equal to 0. Doesn’t this proof not apply to any function that isn’t one-to-one them as delta u will be 0 when delta x is not equal to 0 in a one-to-one function?