What is (\partial)/(\partial x)(4-|x|-|y|) ?

The answer to (\partial)/(\partial x)(4-|x|-|y|) is -x/(|x|)

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(\partial)/(\partial x)(4-|x|-|y|)

\frac{\partial}{\partial x} (4 - ∣ x ∣ - ∣ y ∣)

- \frac{x}{∣ x ∣}

Solution steps

\frac{\partial}{\partial x} (4 - ∣ x ∣ - ∣ y ∣)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (4) - \frac{\partial}{\partial x} (∣ x ∣) - \frac{\partial}{\partial x} (∣ y ∣)

\frac{\partial}{\partial x} (4) = 0

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

\frac{\partial}{\partial x} (∣ y ∣) = 0

= 0 - \frac{x}{∣ x ∣} - 0

Simplify

= - \frac{x}{∣ x ∣}

What is (\partial)/(\partial x)(4-|x|-|y|) ?
The answer to (\partial)/(\partial x)(4-|x|-|y|) is -x/(|x|)