dy÷dx=(x-1)(x+3) at x=2​

Answers

Answer 1

Answer:

[tex]\dfrac{dy}{dx}=\dfrac{4}{25}[/tex]

Explanation:

The given expression is :

[tex]y=\dfrac{(x-1)}{(x+3)}[/tex]

We need to find dy/dx at x = 2

[tex]\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}[/tex]

Put x = 2 in above expression

[tex]\dfrac{dy}{dx}|x=2=\dfrac{4}{(2+3)^2}\\\\=\dfrac{4}{25}[/tex]

Hence, the value at dy/dx is [tex]\dfrac{4}{25}[/tex]


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