en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

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

integral of (3x^2+4x-6)

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

(\partial)/(\partial x)(xcos(xy)-2y)

derivative of cos(xsec^7(x))

integral of 3sin^3(xco)s^2x

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)