Question

10. find dy/dx¹

if y = x³ - 4x²+7x-11
​

Answer 1

Given :

•The given equation is y=x³-4x²+7x-11

To Find :

$\\ \bullet\bf{The \: value \: of \: \dfrac{dy}{dx}=?}$

Formula :

$\\ \bullet \tt \: \frac{d}{dx} {e}^{x} = {e}^{x}$

$\\ \bullet \tt \: \frac{d}{dx} logx = \frac{1}{x}$

$\\ \bullet \tt \: \frac{d}{dx} = {x}^{3} = 3 {x}^{2}$

$\\ \bullet \tt \: \frac{d}{dx} {x}^{n} = n {x}^{n - 1}$

Solution :

The given equation is y=x³-4x²+7x-11

Differentiating both sides with respect to x

$\\ \implies \sf \: y = {x}^{3} - 4 {x}^{2} + 7x - 11 \\ \\ \\ \implies \sf \: \frac{dy}{dx} = \frac{d}{dx} {x}^{3} - \frac{d}{dx} 4 {x}^{2} + \frac{d}{dx} 7x - \frac{d}{dx} 11 \\ \\ \\ \implies \sf \: \frac{dy}{dx} = 3 {x}^{2} - 8x + 7 - 0 \\ \\ \\ \implies \sf \frac{dy}{dx} = 3 {x}^{2} - 8x + 7$

The First Derivative of the given equation is :

$\\ \red \bigstar \boxed{ \sf{ \frac{dy}{dx} = 3 {x}^{2} - 8x + 7}}$