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

The answer to implicit (dy)/(dx),y^2=x-y is (dy)/(dx)= 1/(2y+1)

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implicit (dy)/(dx),y^2=x-y

implicit derivative

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

\frac{d y}{d x} = \frac{1}{2 y + 1}

Solution steps

y^{2} = x - y

Treat

y

y (x)

Differentiate both sides:

2 y \frac{d y}{d x} = 1 - \frac{d y}{d x}

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{1}{2 y + 1}

\frac{d y}{d x} = \frac{1}{2 y + 1}

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

\int tan (u) d u

\frac{d y}{d x} x y = 4

x \to 2 lim (\frac{x ^{3} - 8}{x - 4})

x \to 6 lim (\frac{4}{x - 6})

What is implicit (dy)/(dx),y^2=x-y ?
The answer to implicit (dy)/(dx),y^2=x-y is (dy)/(dx)= 1/(2y+1)