Question

find y'' if x^4+y^4=16​

Answer 1

Answer:

Step-by-step explanation:

Differentiate both sides with respect to x.

4 x^3 + 4y^3 * dy/dx = 0

y'(x) = dy/dx = -x^3/y^3

Now do it again.

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

-x^3*(-3y^4)*dy/dx

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

= -3x^2/y^3 -3x^6*y