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

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Answer 1 · 2016-10-29T06:59:37

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

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, $dy/dx=y*ln(2)*pi*cos(pix)=pi*ln2*cos(pix)*2^(sin(pix))$

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