How do you use implicit differentiation to find (dy)/(dx) given 3x^2+3y^2=2?

2 Answers
Apr 12, 2018

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

Explanation:

Implicit differentiation of the circle 3x^2+3^y^2=2 gives

6x+6y(dy)/(dx)=0.

Solving for (dy)/(dx) gives

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

Apr 12, 2018

dy/dx=-x/y

Explanation:

color(blue)"differentiate implicitly with respect to x"

"noting that"

d/dx(y)=dy/dx" and "d/dx(y^2)=2ydy/dx

rArr6x+6ydy/dx=0

rArr6ydy/dx=-6x

rArrdy/dx=(-6x)/(6y)=-x/y