Question

How do you find the derivative of `f(x) = 1/sqrt(x)`?

Answer 1

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

Explanation:

Remember that `d/dx[x^n]=nx^(n-1)`.

We can rewrite the `f(x)` so that `f(x)=1/(x^(1/2))=x^(-1/2)`.

Using the aforementioned rule, we know that `f'(x)=-1/2x^(-3/2)`.

We can rewrite this as `f'(x)=-1/(2x^(3/2))`.