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):
`x^(4)(5 sin x-3 cos x)`

Explanation

Let `y=x^(4)(5sin x-3 cos x)`
`rArr (dy)/(dx)=(d)/(dx)[x^(4)(5sin x-3 cos x)]`
`=x^(4).(d)/(dx)(5 sin x-3 cos x)`
`+(5 sin x-3 cos x)(d)/(dx)x^(4)`
`=x^(4)(5 cos x+3 sinx)`
`+4x^(3)(5sin x-3 cos x)`
`=x^(3)(x (5 cos x+3 sin x)`
`+4(5 sin x-3 cos x)`
`=x^(3)(5x cos x +3x sin x+20 sin x-12 cos x)`