Question

dy÷dx=(x-1)(x+3) at x=2​

Answer 1

Answer:

$\dfrac{dy}{dx}=\dfrac{4}{25}$

Explanation:

The given expression is :

$y=\dfrac{(x-1)}{(x+3)}$

We need to find dy/dx at x = 2

$\dfrac{dy}{dx}=\dfrac{d}{dx}(\dfrac{x-1}{x+3})\\\\=\dfrac{(x+3)\dfrac{d}{dx}(x-1)-(x-1)\dfrac{d}{dx}(x+3)}{(x+3)^2}\\\\=\dfrac{x+3-(x-1)}{(x+3)^2}\\\\=\dfrac{x+3-x+1}{(x+3)^2}\\\\\dfrac{dy}{dx}=\dfrac{4}{(x+3)^2}$

Put x = 2 in above expression

$\dfrac{dy}{dx}|x=2=\dfrac{4}{(2+3)^2}\\\\=\dfrac{4}{25}$

Hence, the value at dy/dx is $\dfrac{4}{25}$