Question

Find the second derivative at this point

Answer 1

Answer:
`(d^2y)/(dx^2)=(-24)/((-2x-3)^3)`

For this question we are going to use factoring to isolate our y-variable:

`-3y=-3+2xy\\-2xy-3y=-3\\y(-2x-3)=-3\\y=(-3)/(-2x-3)`

Next we are going to take the first and second derivatives, keeping in mind our power and chain rules:

`(d)/(dx)y=(d)/(dx)((-3)/(-2x-3) )\\(dy)/(dx)=(-3)/((-2x-3)^2)(-1)(-2)=((-6)/(-2x-3) )\\(d^2y)/(dx^2)=(-6)/((-2x-3)^3)(-2)(-2)=(-24)/((-2x-3)^3)`