What is (\partial)/(\partial x)(u/x) ?

The answer to (\partial)/(\partial x)(u/x) is -u/(x^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(\partial)/(\partial x)(u/x)

\frac{\partial}{\partial x} (\frac{u}{x})

- \frac{u}{x ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{u}{x})

Treat

u

as a constant

Take the constant out:

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

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= u \frac{\partial}{\partial x} (x^{- 1})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= u (- 1 \cdot x^{- 1 - 1})

Simplify

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

= - \frac{u}{x ^{2}}

What is (\partial)/(\partial x)(u/x) ?
The answer to (\partial)/(\partial x)(u/x) is -u/(x^2)