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

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

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

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

\frac{x - y}{∣ x - y ∣}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

= \frac{x - y}{∣ ( x - y ) ∣} \cdot 1

Simplify

= \frac{x - y}{∣ x - y ∣}

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