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

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

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.
 
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Thank you!
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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