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): `x/(sin^n x)`

Explanation

Given,

`f(x)=x/(sin^nx)`

Now, As we know the derivative of any function

`frac(d(y_1/y_2))dx=frac(y_2d(dy_1/dx)-y_1(dy_2/dx))(y_2^2)`

`impliesfrac(d(x/sin^nx))dx=frac(sin^nxd(dx/dx)-x((dsin^nx)/dx))(sin^(2n)x`

Further solving this we will get

`frac(d(x/sin^nx))dx=frac(sinx-nxcosx)(sin^(n+1)x)`