What is (\partial)/(\partial z)((2x-2z)/(3y+2z)) ?

The answer to (\partial)/(\partial z)((2x-2z)/(3y+2z)) is (-4x-6y)/((3y+2z)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial z)((2x-2z)/(3y+2z))

\frac{\partial}{\partial z} (\frac{2 x - 2 z}{3 y + 2 z})

\frac{- 4 x - 6 y}{( 3 y + 2 z ) ^{2}}

Solution steps

\frac{\partial}{\partial z} (\frac{2 x - 2 z}{3 y + 2 z})

Treat

x, y

as constants

Apply the Quotient Rule:

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

= \frac{\frac{\partial}{\partial z} ( 2 x - 2 z ) ( 3 y + 2 z ) - \frac{\partial}{\partial z} ( 3 y + 2 z ) ( 2 x - 2 z )}{( 3 y + 2 z ) ^{2}}

\frac{\partial}{\partial z} (2 x - 2 z) = - 2

\frac{\partial}{\partial z} (3 y + 2 z) = 2

= \frac{( - 2 ) ( 3 y + 2 z ) - 2 ( 2 x - 2 z )}{( 3 y + 2 z ) ^{2}}

Simplify

\frac{( - 2 ) ( 3 y + 2 z ) - 2 ( 2 x - 2 z )}{( 3 y + 2 z ) ^{2}} : \frac{- 4 x - 6 y}{( 3 y + 2 z ) ^{2}}

= \frac{- 4 x - 6 y}{( 3 y + 2 z ) ^{2}}

\int \frac{4 x}{x ^{2} + 4 x + 4} d x

\frac{d y}{d x} - \frac{4}{x} y = 2 x^{5} e^{\frac{y}{x ^{4}}}

y^{2} = x + 6, y^{2} = 6 - x

\int - 3 x + 2 x d x

n = 0 \sum \infty (2 x + 5)^{n}

What is (\partial)/(\partial z)((2x-2z)/(3y+2z)) ?
The answer to (\partial)/(\partial z)((2x-2z)/(3y+2z)) is (-4x-6y)/((3y+2z)^2)