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

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

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

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

\frac{x + y}{∣ x + y ∣}

Solution steps

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

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)

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

\frac{\partial}{\partial x} (2) = 0

= \frac{x + y}{∣ x + y ∣} - 0

Simplify

= \frac{x + y}{∣ x + y ∣}

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