Question

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)/(sin^(n)x)`

Answer 1

Let `y=(x)/(sin^(n)x)`
`rArr (dy)/(dx)=(d)/(dx)((x)/(sin^(n)x))`
`=(sin^(n)xx(d)/(dx)x-x(d)/(dx)(sin^(n)x))/((sin^(n)x)^(2))`
`=(sin^(n)x.1-x.n sin^(n-1)x.(d)/(Dx)sinx)/(sin^(2n)x)`
`=(sin^(n-1)x[sinx-nxcosx))/(sin^(n+1)x)`