find the derivative of the function

Question

y=4^-x *sinx

Answer 1

y=4^-x sinx  let u = 4^-x and v = sin x

 

u'(x) = -4^-xln 4

v'(x) = cos x

 

Product rule: (uv)' = u'v + uv'

 

So y' = (-4^-xln 4)sin x + (4^-x)cos x; factor, if you like.