Differentiate the following with respect to x:

To Find: Differentiation

NOTE : When 2 functions are in the product then we used product rule i.e

$\frac{d(u, v)}{d x}=v \frac{d u}{d x}+u \frac{d v}{d x}$

Formula used: $\frac{d}{d x}\left(e^{a^{t}}\right)=e^{a^{t}} \times \frac{d}{d x}\left(a^{t}\right)$ and $\frac{d x^{n}}{d x}=n x^{n-1}$

Let us take $y=e^{x^{2}}$

So, by using the above formula, we have

$\frac{d}{d x} e^{x^{2}}=e^{x^{2}} \times \frac{d}{d x}\left(x^{2}\right)=2 x e^{x^{2}}$

Differentiation of $y=e^{x^{2}}$ is $2 x e^{x^{2}}$