Answer
$2x e^{x^2-1}$
Work Step by Step
We have: $f(x)=e^{x^2-1}$
We differentiate both sides with respect to $x$.
$f^{\prime}(x)=\dfrac{d}{dx} [e^{x^2-1}] \\=e^{x^2-1}\dfrac{d}{dx} [x^2-1]\\=e^{x^2-1} \times 2x $
Simplify to obtain:
$f^{\prime}(x)=2x e^{x^2-1}$
