Question

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!!

Answer 1

\[\large \frac{dy}{dx} = \frac{d(e^{\sqrt{x}})}{dx}\]

The chain rule says...take the derivative of the inside...and multiply it to the derivative of the outside...

Take the "inside" to be \(\large \sqrt{x} \)

Answer 2

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

\[\large \frac{e^{\sqrt{x}}}{2\sqrt{x}}\]

Answer 3

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!

Answer 4

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