What is the derivative of (x+y/(xy)) ?

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

What is the first derivative of (x+y/(xy)) ?

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

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

Solution steps

\frac{d}{d x} (\frac{x + y}{x y})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Simplify

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

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

y^{^{'}} = 1 - \frac{y}{20}

7 x^{2} y^{^{'}} = y^{^{'}} + 9 x e - y

\int_{1}^{\infty} \frac{1}{x ^{2} + x} d x

\frac{d}{d x} (2^{x} ln^{2} (2))

9 x + 11, 7 x + 14, [23, 13]

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