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|)