How Do You Apply the Chain Rule to Differentiate y=e^(√x)?

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1. Find the derivative of y=e\sqrt{x}

Homework Equations



Chain rule

The Attempt at a Solution



y=eu

\frac{dy}{du}= ueu-1


u=\sqrt{x}

\frac{du}{dx}= \frac{1}{2}x-1/2

\frac{dy}{dx}= \sqrt{x}e\sqrt{x}-1 × \frac{1}{2}x-1/2

= \sqrt{x} \frac{e^\sqrt{x}}{e} × \frac{1}{2\sqrt{x}}

= \frac{e^\sqrt{x}}{2e}

The answer to this question is \frac{e^\sqrt{x}}{2\sqrt{x}}. What did I do wrong?

Any help is much appreciated.
 
Last edited:
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Nevermind, I got it.

The derivative of e^x is still e^x.
 
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