What is the derivative of 1/(x^2+y^2) ?

The derivative of 1/(x^2+y^2) is -(2x+2y\frac{dy)/(dx)}{(x^2+y^2)^2}

What is the first derivative of 1/(x^2+y^2) ?

The first derivative of 1/(x^2+y^2) is -(2x+2y\frac{dy)/(dx)}{(x^2+y^2)^2}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

- \frac{2 x + 2 y \frac{d y}{d x}}{( x ^{2} + y ^{2} ) ^{2}}

Solution steps

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

- \frac{1}{( x ^{2} + y ^{2} ) ^{2}} \frac{d}{d x} (x^{2} + y^{2})

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

\frac{d}{d x} (x^{2} + y^{2}) = 2 x + 2 y \frac{d y}{d x}

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

Simplify

- \frac{1}{( x ^{2} + y ^{2} ) ^{2}} (2 x + 2 y \frac{d y}{d x}) : - \frac{2 x + 2 y \frac{d y}{d x}}{( x ^{2} + y ^{2} ) ^{2}}

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

x \to \infty lim (- 4 e^{x})

\int \frac{1 + x + x}{x ^{2}} d x

\frac{y ^{3}}{21} + \frac{7}{4 y}

ln (\frac{x}{2})

\frac{( 54 x )}{( x ^{2} + 27 ) ^{2}}

What is the derivative of 1/(x^2+y^2) ?
The derivative of 1/(x^2+y^2) is -(2x+2y\frac{dy)/(dx)}{(x^2+y^2)^2}
What is the first derivative of 1/(x^2+y^2) ?
The first derivative of 1/(x^2+y^2) is -(2x+2y\frac{dy)/(dx)}{(x^2+y^2)^2}