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

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Answer 1 · 2016-06-22T15:32:54

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

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:

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

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