What is the first derivative of x/(|x|) ?

The first derivative of x/(|x|) is 0

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of x/(|x|)

\frac{d}{d x} (\frac{x}{∣ x ∣})

0

Solution steps

\frac{d}{d x} (\frac{x}{∣ x ∣})

Apply the Quotient Rule:

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

= \frac{\frac{d x}{d x} ∣ x ∣ - \frac{d}{d x} ( ∣ x ∣ ) x}{∣ x ∣ ^{2}}

\frac{d x}{d x} = 1

\frac{d}{d x} (∣ x ∣) = \frac{x}{∣ x ∣}

= \frac{1 \cdot ∣ x ∣ - \frac{x}{∣ x ∣} x}{∣ x ∣ ^{2}}

Simplify

\frac{1 \cdot ∣ x ∣ - \frac{x}{∣ x ∣} x}{∣ x ∣ ^{2}} : 0

= 0

\frac{\partial}{\partial x} (π)

- x \frac{d y}{d x} + y = 0

\frac{d ^{2}}{d x ^{2}} (sin (x^{2}))

\int 24 x^{2} + 16 x d x

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