Question

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

Answer 1

`(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`

Answer 2

`dy/dx=-x/y`

Explanation:

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`"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`