How do you implicitly differentiate x^4+2y^2=8 ?

1 Answer
Nov 20, 2015

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

Explanation:

(dx^4)/(dx) = 4x^3

(d2y^2)/(dx) = (d2y^2)/(dy)*(dy)/(dx) = 4y(dy)/(dx)

(d (x^4+2y^2))/(dx) = (dx^4)/(dx)+(d2y^2)/(dx) = 4x^3+4y(dy)/(dx)

(d8)/(dx) = 0

Since x^4+2y^2=8
color(white)("XXX")(d(x^4+2y^2))/(dx) = (d8)/(dx)

color(white)("XXX")4x^3+4y(dy)/(dx)=0

color(white)("XXX")4y(dy)/(dx) = -4x^3

color(white)("XXX")(dy)/(dx) = (-4x^3)/(4y)=-x^3/y