Question

How do you differentiate `2^sin(pi*x)`?

Answer 1

The derivative is `dy/dx=pi*ln2*cos(pix)*2^(sin(pix))`

Explanation:

Let `y=2^(sin(pix))`
Taking the logarithms on both sides

`lny=ln(2^(sin(pix)))=sin(pix)ln2`

So taking the derivatives, we get
`1/ydy/dx=ln(2)*pi*cos(pix)`
So, `dy/dx=y*ln(2)*pi*cos(pix)=pi*ln2*cos(pix)*2^(sin(pix))`