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

[lucphysics]

Homework Statement

f(x)= (sin x)^(sin x)

Homework Equations

The Attempt at a Solution

Taking logarithm on both sides I get:
ln y = ln ((sin x)^(sin x))

 

[Fightfish]

Yes...you are on the right track, why stop there? Simplify the expression and differentiate both sides.

 

[Mark44]

Homework Statement

f(x)= (sin x)^(sin x)

Homework Equations

The Attempt at a Solution

Taking logarithm on both sides I get:
ln y = ln ((sin x)^(sin x))

That's a good start. Can you rewrite the right side by using a property of the natural log function?
After that, you can differentiate both sides of the resulting equation.

 

[lucphysics]

Thank you!