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Calculus/derivatives

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Expert: - 9/3/2009


Question
How do I find the derivative of ln(sinx)?

Answer
It is known that the derivative of g(x) = sinx is g'(x) = cosx.
It is known that the derivative of f(x) = ln(x) is f'(x) = 1/x.

It is known, from the chain rule, that the derivative of f(g(x)) = f'(g(x))g'(x).

From here we can see that f'(g(x)) = 1/g(x) = 1/sinx.

It can also be seen that g'(x) = cosx.

Putting these together gives us an answer of cosx/sinx.  Now we're almost done.

Remember that trig function, cotx = cosx/sinx?  Well, now we're done.

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