(iv) (uv)′ = u′v + uv′ (Leibnitz or product rule)

Let us take u = () and v = ()

Applying Product rule for finding the term xcosx in u’

(gh)′ = g′h + gh′

Taking g = xand h = cosx

[]’ = (1) (cosx) + x (-sinx)

[]’ = cosx – x sinx

Applying the above obtained value for finding u’

u’ = cosx – (cosx – x sinx)

u’ = x sinx

Applying Product rule for finding the term xsinx in v’

(gh)′ = g′h + gh′

Taking g = xand h = sinx

[]’ = (1) (sinx) + x (cosx)

[]’ = sinx + x cosx

Applying the above obtained value for finding v’

v’ = sinx + x cosx - sinx

v’ = x cosx

Putting the above obtained values in the formula:-