Question

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

Answer 1

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

Answer 2

I mean y=e^everything inside your brackets

Answer 3

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

Answer 4

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

Answer 5

following?

Answer 6

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

Answer 7

Yes, you do.

Answer 8

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

Answer 9

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

Answer 10

* = multiplication..

Answer 11

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

Answer 12

where come division comes from ?

Answer 13

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

Answer 14

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