Question

Dy÷dx=(x-1)(x+3) at x=2​

Answer 1

`(dy)/(dx)=(4)/(25)`

Step-by-step explanation:

The given expression is :

`y=((x-1))/((x+3))`

We need to find dy/dx at x = 2

`(dy)/(dx)=(d)/(dx)((x-1)/(x+3))\\\\=((x+3)(d)/(dx)(x-1)-(x-1)(d)/(dx)(x+3))/((x+3)^2)\\\\=(x+3-(x-1))/((x+3)^2)\\\\=(x+3-x+1)/((x+3)^2)\\\\(dy)/(dx)=(4)/((x+3)^2)`

Put x = 2 in above expression

`(dy)/(dx)|x=2=(4)/((2+3)^2)\\\\=(4)/(25)`

Hence, the value at dy/dx is
`(4)/(25)`