What is the derivative of sin x /(1+sin x) ?

Question

please help!!!!!!!!!!!!!!!!!!!!!!!!

Answer 1

The function is sinx/(1+sinx)

Recall the quotient rule of derivatives

d/dx(u/v)=(vu'-uv')/v^2

u=sinx

u'=cosx

v=1+sinx

v'=cosx

d/dx(sinx/(1+sinx)=(1+sinx)(cosx)-(sinx)(cosx)/(1+sinx)^2

                                =cosx+sinxcosx-sinxcosx/(1+sinx)^2

                                =cosx/(1+sinx)^2

Derivative of the given function is cosx/(1+sinx)^2

Answer 2

 

derivative of sin x /(1+sin x)