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.