Question

y=e^(sqrtx).
I need to find the inner and outer function and the derivative of that. calculus problem. I need help with exponents guys.

Answer 1

is e^x outer and sqrtx the inner?

Answer 2

yes

Answer 3

ok what next?

Answer 4

use the chain rule on e^(sqrt[x])

let u = sqrt[x]

\[\frac{ d }{ du }e^u = e^u\]

now \[e^{\sqrt{x}}\frac{ d }{ du }\sqrt{x}\]

Use the power rule (sqrt[x] = x^(1/2)

\[\frac{ d }{ du }x^{1/2} = \frac{ x^{-1/2} }{ 2 }\]

= \[\frac{ 1 }{ 2\sqrt{x} }e^{x}\]

Answer 5

thanks!

Answer 6

np