The derivative of `ln(x+sinx)` with respect to `(x+cosx)` is

Options

A. `(1+cosx)/((x+sinx)(1-sinx))`
B. `(1-cosx)/((x+sinx)(1+sinx))`
C. `(1-cosx)/((x-sinx)(1+cosx))`
D. `(1+cosx)/((x-sinx)(1-cosx))`

Answer

A

Explanation

In(x + sin x) = y
`(dy)/(dx)=(1)/((x + sin x))(1 + cos x)`
`=((1 + cos x))/((x + sin x))`
`x + cos x = z`(say)
`(dz)/(dx)=(1-sin x)`
derivative of In (x + sin x) w.r.t (x + cos x) is
`(dy)/(dz)=((1+cos x))/((x + sin x)(1-sin x))`