First and Second Differentiation Calculation

Differentiation: Questions and Answers

Simple and easy way to differentiate

Differentiation

•         (a) y= 24x³ – 4x⁹ + 3x¹²

y’ = 24(3)x^3-1 – 4(9)x^9-1 + 3(12)x^12-1

y’ = 72x² – 36x⁸ + 36x¹¹(First differentiation)

y’ = 72x² – 36x⁸ + 36x¹¹

y’ = 72(2)x^2-1 – 36(8)x^8-1 + 36(11)x^11-1

y’’ = 144x – 288x⁷ + 396x¹⁰(Second differentiation)

•         (b) y= 10x²(3x + 8)

y= 30x³ + 80x²

y’ = 90x² + 160x

y’’ = 180x + 160

•         (c) y= 27x³/4x

y = 6.75x²(First simplify the question

y’ = 13.5x

y’’ = 13.5