Question

Find d/dx (2^cosx)

Answer 1

\[\frac{d}{dx}a^{f(x)}=a^{f(x)}f'(x)\ln(a)\]

Answer 2

how did you find that?

Answer 3

-ln 2 sin x (2^cos x)

Answer 4

oooohhh i get it thanks guys!

Answer 5

\[y=2^{\cos(x)}\]
Take ln( ) of both sides! :) so we can bring down that function(x).
\[\ln(y)=\cos(x) \ln(2)\]
Now it should be pretty easy to differentiate both sides! :)
\[\frac{y'}{y}=-\sin(x) \ln(2)\]
To find y' multiply y on both sides.
\[y'=-y \sin(x) \ln(2)\]

But \[y=2^{\cos(x)}\]

so we can write
\[y'=-2^{\cos(x)} \sin(x) \ln(2)\]

Answer 6

Thank you so much. I understand that so much more clearly