Given that y= ln cot x, find dy/dx. Hence, find ∫(2-cosec 2x)dx.
Okay basically, I'm stuck on how to differentiate y=ln cot x & then inserting it into the integration equation.
To get dy/dx, use the chain rule (you will also need to use the quotient rule during this process).
I suggest you review some examples from your class notes or textbook (integration by recognition is the name this 'technique' is often given).
If you need more help, please show what you've done and say where you get stuck.
Typo - rather :
(d/dx)cot(x)=(d/dx)[cos(x)/sin(x)]=[-1/sin^2(x)]
And, just in case a picture helps with this part...
Balloon Calculus: standard integrals, derivatives and methods
Hi there,
$\displaystyle \frac{1}{\cot(x)}\ (-\csc^2(x))$
$\displaystyle =\ \tan(x)\ \frac{-1}{\sin^2(x)}$
$\displaystyle =\ \frac{- \sin(x)}{\cos(x) \sin^2(x)}$
$\displaystyle =\ \frac{-1}{\sin(x) \cos(x)}$
$\displaystyle =\ \frac{-1}{\frac{1}{2} \sin(2x)}$
$\displaystyle =\ \frac{-2}{\sin(2x)}$
PS you have a typo in your latest (i.e. should be -2 not 2-, maybe that was the bug).