Question

How do you differentiate `f(x) = (x+sqrtx)^(3/2)` using the chain rule?

Answer 1

The answer is `=3/2(x+sqrtx)^(1/2)*(1+1/(2sqrtx))`

Explanation:

We use `(u^n)'=n u^(n-1)`

The derivative of `f(x)` is

`f'(x)=3/2(x+sqrtx)^(1/2)(x+sqrtx)'`

`=3/2(x+sqrtx)^(1/2)*(1+1/(2sqrtx))`