What is (\partial)/(\partial x)(|x|y+2x) ?

The answer to (\partial)/(\partial x)(|x|y+2x) is (yx)/(|x|)+2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(\partial)/(\partial x)(|x|y+2x)

\frac{\partial}{\partial x} (∣ x ∣ y + 2 x)

\frac{y x}{∣ x ∣} + 2

Solution steps

\frac{\partial}{\partial x} (∣ x ∣ y + 2 x)

Treat

y

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (∣ x ∣ y) + \frac{\partial}{\partial x} (2 x)

\frac{\partial}{\partial x} (∣ x ∣ y) = \frac{y x}{∣ x ∣}

\frac{\partial}{\partial x} (2 x) = 2

= \frac{y x}{∣ x ∣} + 2

What is (\partial)/(\partial x)(|x|y+2x) ?
The answer to (\partial)/(\partial x)(|x|y+2x) is (yx)/(|x|)+2