What is the derivative of 4^[sin(pi*x)]? And how do you go about solving it? thanks

Answer 1

4^[sin(pi*x)] =

exp[log(4) sin(pi x)]

So, by the chain rule, the derivative is:

exp[log(4) sin(pi x)] log(4) pi
cos(pi x) =

pi log(4) 4^[sin(pi x)] cos(pi x)