Question

find the derivative of y=(x+1) (x-2) step by step in notebook ​

Answer 1

Step-by-step explanation:

We have,

$y = (x + 1)(x - 2)$

Taking log both sides,

$\ln(y) = \ln \{ (x + 1)(x - 2) \}$

$\implies\ln(y) = \ln (x + 1) + \ln(x - 2)$

Differentiating both sides, w.r.t x,

$\implies\frac{1}{y}. \frac{dy}{dx} = \frac{1}{ x + 1} + \frac{1}{x - 2}$

$\implies \frac{dy}{dx} = \frac{y}{ x + 1} + \frac{y}{x - 2}$

$\implies \frac{dy}{dx} = \frac{(x + 1)(x - 2)}{ x + 1} + \frac{(x + 1)(x - 2)}{x - 2}$

$\implies \frac{dy}{dx} = x - 2 + x + 1$

$\implies \frac{dy}{dx} = 2x - 1$