Question

How do you find the derivative of `( cos (x) ) / ( 2 + sin (x) )`?

Answer 1

`(-2sinx-1)/(2+sinx)^2`

Explanation:

`f(x)=cosx/(2+sinx)`
let `u(x)=cos(x)` and `v(x)=2+sinx`
then `u'(x)=-sinx` and `v'(x)=cosx`
`f(x)=(u(x))/(v(x))`
`f'(x)=1/(v(x)^2)[v(x)u'(x)-u(x)v'(x)]`
`f'(x)=1/(2+sinx)^2[(2+sinx)(-sinx)-cosx(cosx)]=(-2sinx-1)/(2+sinx)^2`