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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)((xy)/(4x+3y))

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

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

= y \frac{1 \cdot ( 4 x + 3 y ) - 4 x}{( 4 x + 3 y ) ^{2}}

Simplify

y \frac{1 \cdot ( 4 x + 3 y ) - 4 x}{( 4 x + 3 y ) ^{2}} : \frac{3 y ^{2}}{( 4 x + 3 y ) ^{2}}

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

y = sin (x)

\int e^{x} - x^{e} + \frac{5}{x} d x

\int cos (x) cos^{5} (sin (x)) d x

\int \frac{e ^{10 + 3 x}}{5} d x

x \to - 4 lim (- 4)

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