Find the second derivative at this point

Question

asked Jul 3, 2024 99.7k views

1 Answer

Hunterjrj · Answer 1 · 2024-07-07T01:57:01+0000

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:

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