To find: Differentiation of x³ sec x

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

(ii)

(iii)

Let us take u = x³ and v = sec x

Putting the above obtained values in the formula :-

(uv)′ = u′v + uv′

(x³ sec x)’ = 3x²× secx + x³× secx tanx

= 3x²secx + x³secx tanx

= x²secx(3 + x tanx)

Ans) x²secx(3 + x tanx)