To find: Differentiation of (x² + 2x – 3) (x² + 7x + 5)

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

(ii)

Let us take u = (x² + 2x – 3) and v = (x² + 7x + 5)

Putting the above obtained values in the formula :-

(uv)′ = u′v + uv′

[(x² + 2x – 3) (x² + 7x + 5)]’

= (2x + 2) × (x² + 7x + 5) + (x² + 2x – 3) × (2x + 7)

= 2x³ + 14x² + 10x + 2x² + 14x + 10 + 2x³ + 7x² + 4x² + 14x – 6x – 21

= 4x³ + 27x² + 32x – 11

Ans) 4x³ + 27x² + 32x – 11