Finding second derivative

Question

y= (x)/(x^2-9) 

 

I have tried doing it and keep getting the wrong answer. Please show me steps

Answer 1

I will write this in another way to avoid the quotient rule.

 

y = x(x² - 9)^-1

 

 

Take the derivative of y using product rule/chain rule.

 

y' = (x² - 9)^-1 - x(2x)(x² - 9)^-2

 

y' = (x² - 9)^-1 - 2x²(x² - 9)^-2

 

 

Now take the derivative of this derivative.  That is the second derivative.  Continue from here.