What is (\partial)/(\partial x)((xy)/(x+1)) ?

The answer to (\partial)/(\partial x)((xy)/(x+1)) is y/((x+1)^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)/(x+1))

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\frac{( s + 2 )}{( s + 1 ) ^{2}}

\frac{\partial}{\partial z} (x yz + x y^{5} + y z^{5} + z x^{5})

f (x) = 2 e^{3 x}

- 4 e^{4 t}

\frac{\partial}{\partial y} (cos (x))

What is (\partial)/(\partial x)((xy)/(x+1)) ?
The answer to (\partial)/(\partial x)((xy)/(x+1)) is y/((x+1)^2)