Question

What is the derivative of `f(x) = x^(5/2)`?

Answer 1

`f'(x)=5/2x^(3/2)`

Explanation:

We will use the power rule, which states that for any function `f(x)=x^n`, where `n` is a constant, the function's derivative is `f'(x)=nx^(n-1)`.

Thus, the derivative here using `n=5/2` is:

`f'(x)=5/2x^(5/2-1)=5/2x^(3/2)`