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

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Homework Help Overview

The discussion revolves around finding the derivative of the function f(x) = (sin x)^(sin x), which involves logarithmic differentiation and properties of logarithms.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss taking the logarithm of both sides as a method to simplify the differentiation process. There are suggestions to simplify the expression further and to apply properties of logarithms before differentiating.

Discussion Status

Some participants have provided encouragement and guidance on the next steps, emphasizing the importance of simplification and differentiation. The conversation is ongoing, with multiple participants contributing to the exploration of the problem.

Contextual Notes

There is an emphasis on using properties of logarithms in the context of differentiation, but no specific assumptions or constraints have been noted in the discussion.

lucphysics
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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!
 

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