Double derivative of a quotient

[chung963]

Find d^2y/dx^2 when dy/dx = (3x^2 - 24x - 45) ÷ 2y

i tried by (6x-24) ÷ 2y. Unsure what to do about the y on the denominator.

 

[Harrisonized]

dy/dx = (3x²-24x-45) * (2y)^-1

Use the product rule and the chain rule (the derivative of y is dy/dx). After you have that, make a substitution for dy/dx, since you already have that. Of course, you'll also need y², so you also need to integrate using separation of variables to find what y² is.