Question

What is the difference between the chain rule and the power rule? Are they simply different forms of each other?

Answer 1

They are very different !

The "power rule" is used to differentiate a fixed power of `x` e.g. `x^3`

The "chain rule" is used to differentiate a function of a function, e.g. `e^cosx`, `sin(x^3)`, `(1+lnx)^5` etc

Explanation:

Power Rule
`d/dx(x^n)=nx^n-1` where #n' is a constant

Chain Rule

`d/dx(f(g(x) ) = f'(g(x)) * g'(x)` or `dy/dx=dy/(du)*(du)/dx`