Differentiate

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

Let us take u = (x tanx) and v = (secx + tanx)

Applying Product rule for finding u’

(gh)′ = g′h + gh′

Taking g = xand h = tanx

[]’ = (1) (tanx) + x (sec²x)

= tanx + xsec²x

u’ = tanx + xsec²x

Putting the above obtained values in the formula:-