Friday

April 25, 2014

April 25, 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**

Second Derivatives - If y = 2 f(g(x)), then d2y/dx2 = ? The d2y/dx2 means the ...

calculus - Find d2y/dx2 in terms of x and y. y5 = x6

Calc 2 - Find the second derivative (d2y/dx2) for the curve given by x = 2·cos...

maths - x=tcost & y=t+sint then find dx2/d2y

caculus 1, please help - Find d2y/dx2 in terms of x and y. y5 = x6

Calculus - let d2y/dx2= 6x. Find a solution to the differential equation that is...

Maths - If y is a function of x and z = e^z, show that: x (dy/dx) = (dy/dz) and...

integral - Find dy/dx and d2y/dx2 if y= definite integral sign where a= 1 and b...

Integral - Find dy/dx and d2y/dx2 if y= definite integral sign where a= 1 and b...

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