Question

Differentiate it - 1+x² , x⁴ , 3x + 6x² + 7x³ ​

Answer 1

$1. \: - 1 + {x}^{2} \\ \\ \implies \: let \: y = - 1 + {x}^{2} \\ \\ diff. \: w.r.t.x \\ \\ \implies \frac{dy}{dx} = 0 + 2x \\ \\ \implies \frac{dy}{dx} = 2x$

$2. \: {x}^{2} \\ \\ \implies \: let \: y = {x}^{2} \\ \\ diff \: w.r.t.x \\ \\ \implies \: \frac{dy}{dx} = 2x$

$3. \: \: 3x + 6 {x}^{2} + 7 {x}^{3} \\ \\ let \: y = 3x + 6 {x}^{2} + 7 {x}^{3} \\ \\ diff \: w.r.t.x \\ \\ \implies \: \frac{dy}{dx} = 3 + 12x + 21 {x}^{2}$