Question

What is the derivative of `(sinx)/(4+cosx)`?

Answer 1

`(4cosx+1)/(4+cosx)^2`

Explanation:

`"differentiate using the "color(blue)"quotient rule"`

`"Given "y=(g(x))/(h(x))" then"`

`dy/dx=(h(x)g'(x)-g(x)h'(x))/(h(x))^2larrcolor(blue)"quotient rule"`

`g(x)=sinxrArrg'(x)=cosx`

`h(x)=4+cosxrArrh'(x)=-sinx`

`rArrd/dx((sinx)/(4+cosx))`

`=(cosx(4+cosx)+sin^2x)/(4+cosx)^2`

`=(4cosx+cos^2x+sin^2x)/(4+cosx)^2`

`=(4cosx+1)/(4+cosx)^2`