Question

How do you differentiate `f(x) = sin^2 x + 1/2 cot x-tanx`?

Answer 1

`f'(x)=sin(2x)-1/(2sin^2(x))-1/cos^2(x)`

Explanation:

Writing
`f(x)=sin^2(x)+1/2*cos(x)/sin(x)-sin(x)/cos(x)`

`f'(x)=2sin(x)cos(x)+1/2*(-sin^2(x)-cos^2(x))/sin^2(x)-(sin^2(x)+cos^2(x))/cos^2(x)`

so

`f'(x)=sin(2x)-1/(2*sin^2(x))-1/cos^2(x)`