Derivative of Square Root of e to the Power 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 = e^x.

Then, we have

y = √t

By chain rule,

Substitute y = √t and t = e^x.

Substitute t = e^x.

Therefore,

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