What is the derivative of | 1/2 x+1| ?

The derivative of | 1/2 x+1| is (x+2)/(2|x+2|)

What is the first derivative of | 1/2 x+1| ?

The first derivative of | 1/2 x+1| is (x+2)/(2|x+2|)

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

\frac{x + 2}{2 ∣ x + 2 ∣}

Solution steps

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

Simplify

\frac{1}{2} x + 1 : \frac{x}{2} + 1

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

Apply the chain rule:

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

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

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

= \frac{\frac{x}{2} + 1}{( \frac{x}{2} + 1 )} \cdot \frac{1}{2}

Simplify

\frac{\frac{x}{2} + 1}{\frac{x}{2} + 1} \cdot \frac{1}{2} : \frac{x + 2}{2 ∣ x + 2 ∣}

= \frac{x + 2}{2 ∣ x + 2 ∣}

\frac{\partial}{\partial x} (cos (x + 4 y))

200 + \frac{7}{x} + \frac{x ^{2}}{7}

\int \frac{- 4 x + 1}{x ^{2} + 2} d x

\frac{d}{d x} (\frac{9}{( 2 x + 9 ) ^{2}})

\frac{d}{d x} (- 4 sin (4 x))

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