Differentiate y=e^square root (e^2x) sorry bout the "square root" I'm using iPad please show steps for y prime

Question

jamesj · Answer

Do you mean this:
$$ y = \exp(\sqrt{e^{2x}}) $$

anonymous · Answer

I mean y=e^everything inside your brackets

jamesj · Answer

Right.  So use the chain rule.  For example let u(x) = e^2x, then your function is
$$ y = e^{\sqrt{u(x)}} $$

jamesj · Answer

In other words,
$$ \frac{dy}{dx} = \frac{dy}{du} \frac{du}{dx} $$
Now calculate these two terms on the right.

jamesj · Answer

following?

anonymous · Answer

Yeah thanks sorry trying to figure out if I need to use chain rule twice ?

jamesj · Answer

Yes, you do.

anonymous · Answer

Ahhh yeah I get ya :-) thanks heaps for that james

ganpat · Answer

it might be, y = $$y = e ^\sqrt([2x])  * -2\sqrt{x}$$

ganpat · Answer

* = multiplication..

jamesj · Answer

$$ \frac{dy}{du} = \frac{1}{2\sqrt{u}} e^{\sqrt{u}} $$

ganpat · Answer

where come division comes from ?

jamesj · Answer

because the derivative of $ \sqrt{u} $ is $ 1/(2\sqrt{u}) $.

ganpat · Answer

ahhh. k k, i got confuse.. u seems right..