What is (\partial)/(\partial x)((z^2+2x+y)/(xy)) ?

The answer to (\partial)/(\partial x)((z^2+2x+y)/(xy)) is (-z^2-y)/(x^2y)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)((z^2+2x+y)/(xy))

\frac{\partial}{\partial x} (\frac{z ^{2} + 2 x + y}{x y})

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

Solution steps

\frac{\partial}{\partial x} (\frac{z ^{2} + 2 x + y}{x y})

Treat

z, y

as constants

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{y} \frac{\partial}{\partial x} (\frac{z ^{2} + 2 x + y}{x})

Apply the Quotient Rule:

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

= \frac{1}{y} \cdot \frac{\frac{\partial}{\partial x} ( z ^{2} + 2 x + y ) x - \frac{\partial}{\partial x} ( x ) ( z ^{2} + 2 x + y )}{x ^{2}}

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

\frac{\partial}{\partial x} (x) = 1

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

Simplify

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

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

x \to 3 + lim (e^{\frac{2}{3 - x}})

\int x \cdot cos (n x) d x

\int 4 x - 4 x^{2} d x

1 + \frac{9}{25} y^{4}

- 5 t

What is (\partial)/(\partial x)((z^2+2x+y)/(xy)) ?
The answer to (\partial)/(\partial x)((z^2+2x+y)/(xy)) is (-z^2-y)/(x^2y)