## anonymous one year ago y=e^sqrt(x)) x=1 Evaluate dy/dx, meaning they want me to use chain rule, but I cant get the right answer, help!!

1. johnweldon1993

$\large \frac{dy}{dx} = \frac{d(e^{\sqrt{x}})}{dx}$ The chain rule says...take the derivative of the inside...and multiply it to the derivative of the outside... Take the "inside" to be $$\large \sqrt{x}$$

2. johnweldon1993

So if we treat $$\large u = \sqrt{x}$$ ... then $$\large y = e^{u}$$ So the derivative of $$\large \sqrt{x}$$ is $$\large \frac{1}{2\sqrt{x}}$$ and the derivative of $$\large e^{u} = e^{u}$$ So when you multiply them together you get $\large \frac{e^{u}}{2\sqrt{x}}$ But of course you want to go back and replace what 'u' was...so our final answer would be $\large \frac{e^{\sqrt{x}}}{2\sqrt{x}}$

3. anonymous

So simple but somehow I managed to mess this on up, maybe the fact that Ive been studying since 6 am and now its almost 4 pm. Thanks!

4. johnweldon1993

Lol yeah after 2 hours I'm all set...should probably take a break!