1.

Find the derivative of the following functions (it is to be understand that a,b,c,d,p,q,r and s are fixed non-zero constants and m and n are integers): `(cos x)/(1+sin x)`

Answer» Let `y=(cos x)/(1+sin x)`
`rArr (dy)/(dx)=(d)/(dx)((cos x)/(1+sin x))`
`=((1+sin x)(d)/(dx)cos x -cos x(d)/(dx)(1+sin x))/((1+sinx)^(2))`
`=((1+sin x)(-sin x)-cos x.(cos x))/((1+sinx)^(2))`
`=(-sinx-sin^(2)x-cos^(2)x)/((1+sinx)^(2))`
`=(-sinx-(sin^(2)x+cos^(2)x))/(1+sinx)^(2))=(-sinx-1)/((1+sinx)^(2))`
`=(-1(1+sinx))/((1+sinx)^(2))=(-1)/(1+sinx)`


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