What is implicit (dy)/(dx),x^3-xy+y^2=7 ?

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

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implicit (dy)/(dx),x^3-xy+y^2=7

implicit derivative

\frac{d y}{d x}, x^{3} - x y + y^{2} = 7

\frac{d y}{d x} = \frac{- 3 x ^{2} + y}{- x + 2 y}

Solution steps

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

Treat

y

y (x)

Differentiate both sides:

3 x^{2} - 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{- 3 x ^{2} + y}{- x + 2 y}

\frac{d y}{d x} = \frac{- 3 x ^{2} + y}{- x + 2 y}

\frac{d}{d x} (\frac{x - 1}{x})

x \to 0 lim (\frac{9}{x} - \frac{9}{x ^{2} - x})

ln (x) cos (x)

f (x) = (1 + 4 x)^{(\frac{3}{2})}, at x = 2

6 x^{2} - 4 x

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