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Popular >

derivative of |2x-1|

Solution

\frac{d}{d x} (∣ 2 x - 1 ∣)

Solution

\frac{2 ( 2 x - 1 )}{∣ 2 x - 1 ∣}

Solution steps

\frac{d}{d x} (∣ 2 x - 1 ∣)

Apply the chain rule:

\frac{2 x - 1}{∣ ( 2 x - 1 ) ∣} \frac{d}{d x} (2 x - 1)

= \frac{2 x - 1}{∣ ( 2 x - 1 ) ∣} \frac{d}{d x} (2 x - 1)

\frac{d}{d x} (2 x - 1) = 2

= \frac{2 x - 1}{∣ ( 2 x - 1 ) ∣} \cdot 2

Multiply fractions:

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

= \frac{2 ( 2 x - 1 )}{∣ 2 x - 1 ∣}

Popular Examples

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

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

derivative of (x-1^{-2})

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

y^{^{'}} + 3 y = 4 e^{- t}

limit as x approaches 10-of 1/(x-10)

x \to 10 - lim (\frac{1}{x - 10})

integral from-1 to 1 of (3x)/((x+5)^2)

\int_{- 1}^{1} \frac{3 x}{( x + 5 ) ^{2}} d x

Frequently Asked Questions (FAQ)

What is the derivative of |2x-1| ?
The derivative of |2x-1| is (2(2x-1))/(|2x-1|)
What is the first derivative of |2x-1| ?
The first derivative of |2x-1| is (2(2x-1))/(|2x-1|)