Differentiate:
(x2 – 4x + 5) (x3 – 2)
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