Question

How do you find the derivative of:
f(s) = cot x/(1+csc x)

Answer 1

I think the quotient rule would be better

Answer 2

http://en.wikipedia.org/wiki/Quotient_rule

Answer 3

bottom times the derivative of the top - top times derivative of bottom all over bottom squared

Answer 4

this is an annoying problem. change it first to
\[\frac{\cot(x)}{1+\csc(x)}=\frac{\cos(x)}{\sin(x)+1}\] and take the derivative of that with the quotient rule

Answer 5

that one is easy
\[\frac{-(\sin(x)+1)\times \sin(x)-(\cos^2(x))}{(\sin(x)+1)^2}\]
\[\frac{-\sin^2(x)-\sin(x)-\cos^2(x)}{(\sin(x)+1)^2}\]
\[\frac{-\sin(x)-1}{(\sin(x)+1)^2}\]
\[-\frac{1}{\sin(x)+1}\]

Answer 6

thank you