What is the derivative of |2x| ?

The derivative of |2x| is (2x)/(|x|)

What is the first derivative of |2x| ?

The first derivative of |2x| is (2x)/(|x|)

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\frac{d}{d x} (∣ 2 x ∣)

\frac{2 x}{∣ x ∣}

Solution steps

\frac{d}{d x} (∣ 2 x ∣)

Simplify

∣ 2 x ∣ : 2 ∣ x ∣

= \frac{d}{d x} (2 ∣ x ∣)

Take the constant out:

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

= 2 \frac{d}{d x} (∣ x ∣)

Apply the common derivative:

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

= 2 \cdot \frac{x}{∣ x ∣}

Multiply fractions:

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

= \frac{2 x}{∣ x ∣}

\frac{d}{d x} ((1 + 2 x)^{- \frac{1}{2}})

10 - 3 x

\int (cos (θ) sin (θ)) d θ

y = x^{2}, y = 9 x

\frac{d}{d x} (\frac{11}{( 2 x + 1 ) ^{2}})

What is the derivative of |2x| ?
The derivative of |2x| is (2x)/(|x|)
What is the first derivative of |2x| ?
The first derivative of |2x| is (2x)/(|x|)