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

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

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

implicit derivative

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

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

Solution steps

y = - \frac{x}{y}

Treat

y

y (x)

Differentiate both sides:

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

Isolate

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

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

\int e^{\frac{- x ^{2}}{2}} d x

\frac{d}{d t} (\frac{2 t}{1 + 4 t ^{2}})

\int_{0}^{1} π (2 x^{2})^{2} d x

y^{^{''}} + 4 y = 2 sec (2 t)

4 x^{2} + 5 x, at x = 3

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