Answer
$f'(x^2) = \frac{x}{2}$
Work Step by Step
We solve for $f'(x^2)$ as follows:
$\frac{d}{dx} [f(x^2)] = f'(x^2) *(\frac{d}{dx}[x^2]) = f'(x^2) * (2x)$
From the problem, $\frac{d}{dx} [f(x^2)] = x^2$.
Thus, we equate the two equivalent expressions:
$f'(x^2) * (2x) = x^2$
$f'(x^2) = \frac{x}{2}$
