What is the derivative of (sin x)^(3x)?

1 Answer
Dec 6, 2016

3(sinx)^(3x)(lnsinx+xcotx)

Explanation:

y=(sinx)^(3x)
taking ln both sides
lny=ln(sinx)^(3x)
lny=(3x)ln(sinx)
Differentiate both sides
(1/y)dy/dx=3lnsinx+3x(1/sinx)cosx
dy/dx=(3lnsinx+3xcotx)y
putting value of y
dy/dx=3(lnsinx+xcotx)(sinx)^(3x)
it can be written as
dy/dx=3(sinx)^(3x)(lnsinx+xcotx)