Find derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): `(4x+5sinx)/(3x+7cosx)`

Explanation

Let `y=(4x+5 sinx)/(3x+7cos x)`
`rArr(dy)/(dx)=(d)/(dx)[((4x+5sinx)/(3x+7cos x)]`
`(3x+7cos x)(d)/(dx)(4x+5 sinx)`
`=(-(4x+5sinx)(d)/(dx)(3x+7cos x))/((3x+7 cos x)^(2))`
`(12x+15x cos x+28 cos x+35cos^(2)x)`
`=(-(12x-28xsinx+15sinx-35sin^(2)x)+28x sin x-15 sin x)/((3x+7 cos x)^(2))`
`15x cos x +28 cos x +35`
`=(15x cos x+28 cos x+35+28xsinx-15sinx)/((3x+7cos x)^(2))`