What is the derivative of 1-|1-x| ?

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

What is the first derivative of 1-|1-x| ?

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

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\frac{d}{d x} (1 - ∣ 1 - x ∣)

\frac{- x + 1}{∣ - x + 1 ∣}

Solution steps

\frac{d}{d x} (1 - ∣ 1 - x ∣)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d x} (1) = 0

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

= 0 - (- \frac{1 - x}{∣ 1 - x ∣})

Simplify

= \frac{- x + 1}{∣ - x + 1 ∣}

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