How do you use implicit differentiation to find (dy)/(dx)dydx given 3x^2+3y^2=23x2+3y2=2?

2 Answers
Apr 12, 2018

(dy)/(dx)=-x/ydydx=xy

Explanation:

Implicit differentiation of the circle 3x^2+3^y^2=23x2+3y^2=2 gives

6x+6y(dy)/(dx)=06x+6ydydx=0.

Solving for (dy)/(dx)dydx gives

(dy)/(dx)=-x/ydydx=xy

Apr 12, 2018

dy/dx=-x/ydydx=xy

Explanation:

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

"noting that"noting that

d/dx(y)=dy/dx" and "d/dx(y^2)=2ydy/dxddx(y)=dydx and ddx(y2)=2ydydx

rArr6x+6ydy/dx=06x+6ydydx=0

rArr6ydy/dx=-6x6ydydx=6x

rArrdy/dx=(-6x)/(6y)=-x/ydydx=6x6y=xy