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

[physics604]

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

Homework Equations

Chain rule

The Attempt at a Solution

y=e^u

\frac{dy}{du}= ue^u-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.

 

[physics604]

Nevermind, I got it.

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