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Find derivative of the following functio...

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)`

Text Solution

Verified by Experts

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)`
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