To find: Differentiation of xⁿ cot x

Formula used: (i) (uv)′ = u′v + uv′ (Leibnitz or product rule)

(ii)

(iii)

Let us take u = xⁿ and v = cotx

Putting the above obtained values in the formula :-

(uv)′ = u′v + uv′

(xⁿ cotx)’ = nx^n-1× cotx + xⁿ× -cosec²x

= nx^n-1cotx - xⁿcosec²x

= xⁿ (nx^-1cotx - cosec²x)

Ans) xⁿ (nx^-1cotx - cosec²x)