Question

Medal and Fan..
show step by step full solution:
Derivative of (sin 2x) ^ (e^x)

Answer 1

\[(\sin 2x)^{e ^{x}}\]

Answer 2

@modphysnoob can you please explain that?

Answer 3

ok

Answer 4

@phi

Answer 5

try taking the ln first

Answer 6

\[y=\left(\sin x\right)^{e^x}\\
\ln y=\ln (\sin x)^{e^x}\\
\ln y=e^x \ln \sin x\]
Then apply some implicit differentiation.

Answer 7

@SithsAndGiggles how about the 2x?

Answer 8

Sorry, minor typo. Just make sure to account for it:
\[\frac{d}{dx}\ln y=\frac{d}{dx}\left[e^x\ln \sin2x\right]\]

Answer 9

I still need to derive sin 2x right?

Answer 10

Yes. The right side will involve product rule first, then chain rule as you deal with \(\ln \sin 2x\).

Answer 11

ok, i will try..