Question

How do you differentiate `f(x)=(x^2-cosx/x)/sinx` using the quotient rule?

Answer 1

if F(x)= `u/v`
the formula goes as follows:

F'(x)= `{(u)'.(v)-(v)'.(u)}/(v)^2`
so,
(u)'= `2x`
(v)'=`[(-sinx)x-cosx]/x^2`
F'(x)= `{(2x)-[(-sinx)x-cosx]/x^2}(sinx)-(cosx)[x^2-cosx/x]}/sin^2x`
now you can solve it further