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Popular >

implicit 2xy-y^2=-1

Solution

implicit derivative

2 x y - y^{2} = - 1

Solution

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

Solution steps

2 x y - y^{2} = - 1

Treat

y

as

y (x)

Differentiate both sides:

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{y}{x - y}

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

Popular Examples

derivative of cos^4(4x^2+1)

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

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\int (3 x^{2} + 4 x - 6) d x

derivative of-1/3 (x^{-3}-x^6)

\frac{d}{d x} (- \frac{1}{3} (x^{- 3} - x^{6}))

derivative of sqrt(33+4t)derivative of

33 + 4 t

derivative of (x^2)/((4+x))derivative of

\frac{x ^{2}}{( 4 + x )}

Frequently Asked Questions (FAQ)

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