What is (\partial)/(\partial x)((5xy)/(10x-y)) ?

The answer to (\partial)/(\partial x)((5xy)/(10x-y)) is -(5y^2)/((10x-y)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)((5xy)/(10x-y))

\frac{\partial}{\partial x} (\frac{5 x y}{10 x - y})

- \frac{5 y ^{2}}{( 10 x - y ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{5 x y}{10 x - y})

Treat

y

as a constant

Take the constant out:

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

= 5 y \frac{\partial}{\partial x} (\frac{x}{10 x - y})

Apply the Quotient Rule:

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

= 5 y \frac{\frac{\partial}{\partial x} ( x ) ( 10 x - y ) - \frac{\partial}{\partial x} ( 10 x - y ) x}{( 10 x - y ) ^{2}}

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

\frac{\partial}{\partial x} (10 x - y) = 10

= 5 y \frac{1 \cdot ( 10 x - y ) - 10 x}{( 10 x - y ) ^{2}}

Simplify

5 y \frac{1 \cdot ( 10 x - y ) - 10 x}{( 10 x - y ) ^{2}} : - \frac{5 y ^{2}}{( 10 x - y ) ^{2}}

= - \frac{5 y ^{2}}{( 10 x - y ) ^{2}}

x \to \frac{π}{2} lim (x sec (x))

\frac{4}{s ( s + 2 ) ^{3}}

\int e^{l n (t)} d t

\int - cot (x) d x

\int \frac{35}{x ^{3} - 27} d x

What is (\partial)/(\partial x)((5xy)/(10x-y)) ?
The answer to (\partial)/(\partial x)((5xy)/(10x-y)) is -(5y^2)/((10x-y)^2)