Differentiate:

e^x cos x

To find: Differentiation of e^x cos x

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

(ii)

(iii)

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

Putting the above obtained values in the formula:-

(uv)′ = u′v + uv′

(e^x cosx)’ = e^x× cosx + e^x× -sinx

= e^xcosx - e^xsinx

= e^x (cosx - sinx)

Ans) e^x (cosx - sinx)