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

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

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(\partial)/(\partial x)(|xy|)

\frac{\partial}{\partial x} (∣ x y ∣)

\frac{x ∣ y ∣}{∣ x ∣}

Solution steps

\frac{\partial}{\partial x} (∣ x y ∣)

Simplify

∣ x y ∣ : ∣ x ∣ ∣ y ∣

= \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 t} (e^{- 6 t})

y^{^{'}} - 6 + \frac{y}{( 4 ( x + 250 ) )} = 0, y (0) = 70

\int 2 x sec (4 x^{2}) d x

\int_{0}^{1} \frac{e ^{x}}{16 - e ^{2 x}} d x

\int - sin (n x) d x

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