What is implicit 3x^2+xy+3y^2=7 ?

The answer to implicit 3x^2+xy+3y^2=7 is (dy)/(dx)=(-6x-y)/(x+6y)

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implicit 3x^2+xy+3y^2=7

implicit derivative

3 x^{2} + x y + 3 y^{2} = 7

\frac{d y}{d x} = \frac{- 6 x - y}{x + 6 y}

Solution steps

3 x^{2} + x y + 3 y^{2} = 7

Treat

y

y (x)

Differentiate both sides:

6 x + y + x \frac{d y}{d x} + 6 y \frac{d y}{d x} = 0

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{- 6 x - y}{x + 6 y}

\frac{d y}{d x} = \frac{- 6 x - y}{x + 6 y}

What is implicit 3x^2+xy+3y^2=7 ?
The answer to implicit 3x^2+xy+3y^2=7 is (dy)/(dx)=(-6x-y)/(x+6y)