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

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

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

implicit derivative

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

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

Solution steps

(x - y)^{2} = 2 a x

Treat

y

y (x)

Differentiate both sides:

2 (x - y) (1 - \frac{d y}{d x}) = 2 a

Isolate

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

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

\frac{d}{d x} (\frac{x ^{3}}{x ^{2} + 2})

\frac{d}{d x} (2 x^{3} - 6 x^{2})

y^{^{'}} = y (1 - 0.0002 y)

\frac{1}{( s + 2 ) ( s ^{2} - 2 s + 5 )}

\int_{- 3}^{- 1} x^{2} e^{x^{3} + 27} d x

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