Derivative of e to the Power of Square Root x

We know the derivative of ex, which is ex.

(ex)' = ex

We can find the derivative of ex using chain rule.

If y = ex, find ᵈʸ⁄d.

Let t = √x.

Then, we have

y = et

By chain rule,

Substitute y = et and t = √x.

Substitute t = √x.

Therefore,

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