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

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

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

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

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\frac{d}{d x} (∣ x ∣ + ∣ x - 1 ∣)

\frac{x}{∣ x ∣} + \frac{x - 1}{∣ x - 1 ∣}

Solution steps

\frac{d}{d x} (∣ x ∣ + ∣ x - 1 ∣)

Apply the Sum/Difference Rule:

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

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

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

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

= \frac{x}{∣ x ∣} + \frac{x - 1}{∣ x - 1 ∣}

\frac{d}{d x} (x tan (2 x))

\frac{\partial}{\partial x} (sin (x^{3}))

x \to 3 + lim (\frac{2 x + 1}{x - 3})

\int sin (4 π t) d t

\int 2 t^{4} + 2 d t

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