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:
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)
It is stated as below :
To let you visualize it, if you let , it'll be :
So here, what do you have ?
so f is the logarithm function.
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
Visual AND formal...
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