What is (\partial)/(\partial x)((5x+4y)/(3x+2y)) ?

The answer to (\partial)/(\partial x)((5x+4y)/(3x+2y)) is -(2y)/((3x+2y)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)((5x+4y)/(3x+2y))

\frac{\partial}{\partial x} (\frac{5 x + 4 y}{3 x + 2 y})

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

Solution steps

\frac{\partial}{\partial x} (\frac{5 x + 4 y}{3 x + 2 y})

Treat

y

as a constant

Apply the Quotient Rule:

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

= \frac{\frac{\partial}{\partial x} ( 5 x + 4 y ) ( 3 x + 2 y ) - \frac{\partial}{\partial x} ( 3 x + 2 y ) ( 5 x + 4 y )}{( 3 x + 2 y ) ^{2}}

\frac{\partial}{\partial x} (5 x + 4 y) = 5

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

= \frac{5 ( 3 x + 2 y ) - 3 ( 5 x + 4 y )}{( 3 x + 2 y ) ^{2}}

Simplify

\frac{5 ( 3 x + 2 y ) - 3 ( 5 x + 4 y )}{( 3 x + 2 y ) ^{2}} : - \frac{2 y}{( 3 x + 2 y ) ^{2}}

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

\int (tan (x))^{2} sec (x) d x

\frac{\partial}{\partial x} (6 - x^{3} - y^{5})

\frac{d}{d x} (arcsec (7 x))

\frac{2 x ^{2} + 4 x}{( x + 1 ) ^{2}}

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

What is (\partial)/(\partial x)((5x+4y)/(3x+2y)) ?
The answer to (\partial)/(\partial x)((5x+4y)/(3x+2y)) is -(2y)/((3x+2y)^2)