Question:

f(x) = ln(cosx)

I need to find the derivative.

I'm unsure where to start. I tried the chain rule, and I get stuck, as follows:

The answer is supposed to be -tanx

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- June 11th 2010, 05:43 AMGlitchDerivative help
Question:

f(x) = ln(cosx)

I need to find the derivative.

I'm unsure where to start. I tried the chain rule, and I get stuck, as follows:

The answer is supposed to be -tanx - June 11th 2010, 05:48 AMpickslides
- June 11th 2010, 05:52 AMGlitch
Interesting. So that's the chain rule? Your working out isn't very familiar to me.

- June 11th 2010, 06:04 AMRaoh
- June 11th 2010, 06:11 AMGlitch
I find the derivative of g(x), then the derivative of f(g(x)), then multiply them. I think the bit that confuses me is since the function is the natural logarithm, you don't lower the power like I did in the OP. Or maybe you do, and I'm going nuts.

- June 11th 2010, 06:22 AMRaoh
- June 11th 2010, 06:26 AMGlitch
Yeah, I made an error. Thanks for the help!

- June 18th 2010, 06:48 AMchisigma
A general formula for the 'logarithmic derivative' of a function is...

d/dx ln f(x) = f'(x)/f(x) (1)

... and here is f(x) = cos x , so that...

Kind regards

- June 18th 2010, 07:58 AMTheCoffeeMachine
Why were you lowering the power, though? The derivative of ln{x} is 1/{x} and the derivative of cosx is -sinx. That should be sufficient:

http://latex.codecogs.com/gif.latex?...0=%20-\tan{x}.