Posted by **Jin** on Monday, September 25, 2006 at 5:14pm.

I am finding the second derivative of (x^2)(y^3) = 1

2x(y^3) + (x^2)(y')(3y^2) = 0

And I simplified the answer to

y'= (-2y)/(3x)

so it would be...

[(-2y')(3x)-(-2y)(3)]/(9x^2) and it's simplified to (-6xy'+6y)/(9x^2)= y''

I could plug in (-2y)/(3x) in place of y'.

The correct answer is y''=(10y)/(9x^2), but I did not get this answer. Please help me!

This looks correct, but you dropped the y'

2x(y^3) + (x^2)(y')(3y^2)y' = 0 so

y'=-2x(y^3)/(x^2)(3y^2)=-2y/3x

If we now differentiate this again we get

y"=[3x*(-2y')-(-2y)*3]/(9x^2)=(-6xy'+6y)/(9x^2)

If we now substitute -2y/3x for y' we get

y"=[(-6x*-2y/3x)+6y]/9x^2=[4y+6y]/9x^2

Yes, you should make the substitution for y' and you'll get the correct answer in terms of x and y only.

## Answer this Question

## Related Questions

- check my work on derivatives - Can someone check my work? So, I took the ...
- Calculus - How would I go about finding the derivative of f(x)=ln(x)(7x-2)^3 ...
- Calculus (Help) - Also I would like to know how to set this problem up in ...
- Calculus - R=M^2(c/2-m/3) dR/dM=CM-M^2 I found the derivative. Now how would I ...
- Calculus - f(x)=x^3(x^(4)-8) Find f '(x) by multiplying out before taking the ...
- Calc-please help! - What is the second derivative of (x^3)/(x^2-1)? And how ...
- Calculus--> bobpursley - How do you get m=0? from taking the second ...
- Derivatives- Math - Can someone explain how to find the derivative of : 1. y= 5...
- math - use the quotient rule to find derivative. y= 3x^2+8 / x^2+3 (x^2+3)(6x...
- Calc I - if f(t)=sqrt(4t+1) find f''(2) I got the first derivative to be: 1/2(4t...