I want to integrate -ln|cos(x)|+k, I and I should end with tan(x).

However, I'm stuck. I don't know what I need to do after

This is how far I've gotten so far:

http://img504.imageshack.us/img504/6739/tanjf9.gif

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- Dec 1st 2008, 06:37 AMNo Logic SenseDifferentiating
I want to integrate -ln|cos(x)|+k, I and I should end with tan(x).

However, I'm stuck. I don't know what I need to do after

This is how far I've gotten so far:

http://img504.imageshack.us/img504/6739/tanjf9.gif - Dec 1st 2008, 09:34 AMrunning-gag
Hello

Something I do not understand : the title of your post is "differentiating" and you want to integrate -ln|cos(x)|+k ?

I think that you want to differentiate -ln|cos(x)|+k

Differentiating ln(u(x)) gives u'(x) / u(x)

Here it gives sin(x)/cos(x) = tan(x) - Dec 1st 2008, 10:32 AMMoo
Hello,

I think you have a little problem with the chain rule of differentiation.

It is stated as below :

To let you visualize it, if you let , it'll be :

So here, what do you have ?

so

so f is the logarithm function.

and

by using the formula, you'll have the derivative of your function :

it's not formal, but it helps you understand how to use the formula.

Note that you just have to multiply the final result by -1 to get the derivative you're looking for - Dec 1st 2008, 11:10 AMtom@ballooncalculus
Visual AND formal...

http://www.ballooncalculus.org/mhf24.gif

As usual, straight continuous lines differentiate with respect to x and the straight dashed line with respect to the dashed balloon expression, so that the triangular network satisfies the chain rule.

Don't integrate - balloontegrate! Balloon Calculus: worked examples from past papers