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

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

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

\frac{\partial}{\partial x} (∣ x ∣ y)

\frac{x y}{∣ x ∣}

Solution steps

\frac{\partial}{\partial x} (∣ x ∣ y)

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the common derivative:

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

= y \frac{x}{∣ x ∣}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{x y}{∣ x ∣}

\frac{d}{d x} (\frac{e ^{3 x} + e ^{x^{2}}}{3})

\int e^{- 3 x} + 2 x d x

\int \frac{- x}{x ^{2} + 4} d x

x \to 1 lim (2 x - 1)

f (x) = 3 x - 2 x^{2}

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