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

The answer to (\partial)/(\partial x)((3x-y)/(x+2y)) is (7y)/((x+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)((3x-y)/(x+2y))

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

\frac{7 y}{( x + 2 y ) ^{2}}

Solution steps

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

\frac{\partial}{\partial x} (3 x - y) = 3

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

= \frac{3 ( x + 2 y ) - 1 \cdot ( 3 x - y )}{( x + 2 y ) ^{2}}

Simplify

\frac{3 ( x + 2 y ) - 1 \cdot ( 3 x - y )}{( x + 2 y ) ^{2}} : \frac{7 y}{( x + 2 y ) ^{2}}

= \frac{7 y}{( x + 2 y ) ^{2}}

\int \frac{cos ( x )}{sin ( x ) + sin ^{2} ( x )} d x

y^{^{''}} + 34 y = 0

d x + d y e^{6 x} = 0

f (x) = e^{1}

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

What is (\partial)/(\partial x)((3x-y)/(x+2y)) ?
The answer to (\partial)/(\partial x)((3x-y)/(x+2y)) is (7y)/((x+2y)^2)