Derivative of e to the Power x Square

We know the derivative of ex, which is ex.

(ex)' = ex

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

Find ᵈʸ⁄d, if

Let t = x2.

Then, we have

y = et

Now, y = et 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 :

Substitute y = et and t = x2.

Substitute t = x2.

Therefore,

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