To find: Differentiation of e^x cot x

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

(ii)

(iii)

Let us take u = e^x and v = cotx

Putting the above obtained values in the formula:-

(uv)′ = u′v + uv′

(e^x cotx)’ = e^x× cotx + e^x× -cosec²x

= e^xcotx - e^xcosec²x

= e^x (cotx - cosec²x)

Ans) e^x (cotx - cosec²x)