What is (\partial)/(\partial x)(((xv^2))/((x^2+v^2))) ?

The answer to (\partial)/(\partial x)(((xv^2))/((x^2+v^2))) is (v^2(-x^2+v^2))/((x^2+v^2)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)(((xv^2))/((x^2+v^2)))

\frac{\partial}{\partial x} (\frac{( x v ^{2} )}{( x ^{2} + v ^{2} )})

\frac{v ^{2} ( - x ^{2} + v ^{2} )}{( x ^{2} + v ^{2} ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{( x v ^{2} )}{( x ^{2} + v ^{2} )})

Treat

v

as a constant

Take the constant out:

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

= v^{2} \frac{\partial}{\partial x} (\frac{x}{x ^{2} + v ^{2}})

Apply the Quotient Rule:

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

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

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

\frac{\partial}{\partial x} (x^{2} + v^{2}) = 2 x

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

Simplify

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

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

(\frac{x + 2}{x}) (7 - 2 x^{3})

\int \frac{5}{( 5 x + 4 ) ln ( 5 x + 4 )} d x

\int 6 x^{2} - 2 x + 1 d x

n = 1 \sum \infty \frac{n}{n ^{3} + 3}

What is (\partial)/(\partial x)(((xv^2))/((x^2+v^2))) ?
The answer to (\partial)/(\partial x)(((xv^2))/((x^2+v^2))) is (v^2(-x^2+v^2))/((x^2+v^2)^2)