What is the derivative of |2x-3| ?

The derivative of |2x-3| is (2(2x-3))/(|2x-3|)

What is the first derivative of |2x-3| ?

The first derivative of |2x-3| is (2(2x-3))/(|2x-3|)

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\frac{d}{d x} (∣ 2 x - 3 ∣)

\frac{2 ( 2 x - 3 )}{∣ 2 x - 3 ∣}

Solution steps

\frac{d}{d x} (∣ 2 x - 3 ∣)

Apply the chain rule:

\frac{2 x - 3}{∣ ( 2 x - 3 ) ∣} \frac{d}{d x} (2 x - 3)

= \frac{2 x - 3}{∣ ( 2 x - 3 ) ∣} \frac{d}{d x} (2 x - 3)

\frac{d}{d x} (2 x - 3) = 2

= \frac{2 x - 3}{∣ ( 2 x - 3 ) ∣} \cdot 2

Multiply fractions:

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

= \frac{2 ( 2 x - 3 )}{∣ 2 x - 3 ∣}

\frac{d}{d x} (25 e^{5 x})

\frac{\partial}{\partial x} (\frac{31 x y}{x - y})

\int sec^{2} (θ) tan^{8} (θ) d θ

\frac{\partial}{\partial x} (1 + y^{2})

9 y^{^{''}} - 6 y^{^{'}} + y = 0

What is the derivative of |2x-3| ?
The derivative of |2x-3| is (2(2x-3))/(|2x-3|)
What is the first derivative of |2x-3| ?
The first derivative of |2x-3| is (2(2x-3))/(|2x-3|)