What is implicit (dy)/(dx),x^2+xy+y^2=7 ?

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

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implicit (dy)/(dx),x^2+xy+y^2=7

implicit derivative

\frac{d y}{d x}, x^{2} + x y + y^{2} = 7

\frac{d y}{d x} = \frac{- 2 x - y}{x + 2 y}

Solution steps

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

Treat

y

y (x)

Differentiate both sides:

2 x + y + x \frac{d y}{d x} + 2 y \frac{d y}{d x} = 0

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{- 2 x - y}{x + 2 y}

\frac{d y}{d x} = \frac{- 2 x - y}{x + 2 y}

\int_{0}^{\frac{π}{3}} 2 sec^{2} (x) d x

f (x) = x + 3, g (x) = \frac{1}{2} x + 3

\int_{0}^{5} \frac{1}{( 5 - x ) ^{\frac{1}{3}}} d x

3 x^{4} - 7 ln (x)

\int \frac{x ^{4} + 2 x ^{3} - 3}{x ^{3}} d x

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