Derivative of e to the Power of Square Root x

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

(e^x)' = e^x

We can find the derivative of e^√x using chain rule.

If y = e^√x, find ᵈʸ⁄dₓ.

Let t = √x.

Then, we have

y = e^t

By chain rule,

Substitute y = e^t and t = √x.

Substitute t = √x.

Therefore,

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