Friday

August 29, 2014

August 29, 2014

Posted by **Anonymous** on Thursday, March 1, 2012 at 11:37pm.

I got the first derivative which was x^3/y^3 and no im am stuck on using implicit differentiation for the second derivative part

- calculus -
**Steve**, Friday, March 2, 2012 at 2:18pmy^4 - x^4 = 16

4y^3 y' - 4x^3 = 0

y' = x^3/y^3

y'' = (3x^2*y^3 - x^3*3y^2*y')/y^6

= 3x^2(y-xy')/y^4

= 3x^2 (y-x*x^3/y^3)/y^4

= 3x^2 (y^4 - x^4)/y^7

= 48x^2/y^7

or,

y^3 y' = x^3

3y^2 y'^2 + y^3 y'' = 3x^2

3y^2 (x^6/y^6) + y^3 y'' = 3x^2

y^3 y'' = 3x^2 - 3x^6/y^4

y'' = 3x^2 (y^4 - x^4)/y^7

**Related Questions**

Calculus 1 - implicit differentiation - I do not understand implicit ...

Calculus 1 - implicit differentiation - I do not understand implicit ...

Calculus Help STEVE - find y'' by implicit differentiation. 2x^3 + 3y^3 = 8 I ...

calculus - Alright so implicit differentiation is just not working out for me. ...

Math - Calculus Question. - hey can someone explain to me the relationship ...

Implicit differentiation calculus - PLEASE HELP , I DON'T UNDERSTAND find dy/dx ...

Calculus: implicit differentiation - Find dy/dx by implicit differentiation 1. x...

calculus; implicit differentiation - Use implicit differentiation to find the ...

Calculus 1 Implicit differentiation - Help please help me understand what i am ...

Calculus - How do you use imlicit differentiation to differentiate e^(xy)? I ...