Question

LGBADERIVATIVES!!

\[\Large y = 2^{\sin \pi x}\]

Answer 1

im thinking ln first

Answer 2

so this is the in form a^u

Answer 3

(ln|a|)a^u * u'

Answer 4

\[\ln y = \ln (\sin \pi x) \ln 2\]

Answer 5

\[ \large y'=2^{\sin\pi x}(\ln 2)(\cos\pi x)\pi \]

Answer 6

We know that
\[\frac{d}{dx} a^x=a^x \times \ln a\]
Here we have
\[\large y=2^{\sin (\pi x)}\]
Let's differentiate this
\[\frac{dy}{dx}= 2^{\sin (\pi x)} \times \ln 2 \times \frac{d}{dx} (\sin \pi x)\times \frac{d}{dx} (\pi x)\]

Answer 7

\[\LARGE \frac 1y y' = \frac{1}{\sin \pi x} \cos \pi x \ln 2?\]

Answer 8

there is no need for implicit derivatives

Answer 9

no?

Answer 10

just apply the chain rule!

Answer 11

actually a^u is implicit derivatives....

Answer 12

however i think there should be a 1/sin pi x somewhere...

Answer 13

oh wait i did it wrong

Answer 14

nevermind

Answer 15

i'm pretty sure a^u is supposed to be int here a swell.