To find: Differentiation of (x² – 4x + 5) (x³ – 2)

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

(ii)

Let us take u = (x² – 4x + 5) and v = (x³ – 2)

Putting the above obtained values in the formula:-

(uv)′ = u′v + uv′

[(x² – 4x + 5) (x³ – 2)]’ = (2x – 4)×(x³ – 2) + (x² – 4x + 5)×(3x²)

= 2x⁴ – 4x - 4x³ + 8 + 3x⁴ – 12x³ + 15x²

= 5x⁴ - 16x³ + 15x² – 4x + 8

Ans) 5x⁴ - 16x³ + 15x² – 4x + 8