Derivative of e to the Power x Square

We know the derivative of e^x, which is e^x.

(e^x)' = e^x

We can find the derivative of e to power x² using chain rule.

Find ᵈʸ⁄dₓ, if

Let t = x².

Then, we have

y = e^t

Now, y = e^t and t = x². That is, y is a function of t and t is a function of x.  

By chain rule, the derivative of y with respect to x :

Substitute y = e^t and t = x².

Substitute t = x².

Therefore,

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