What is the derivative of 5-|x-5| ?

The derivative of 5-|x-5| is -(x-5)/(|x-5|)

What is the first derivative of 5-|x-5| ?

The first derivative of 5-|x-5| is -(x-5)/(|x-5|)

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\frac{d}{d x} (5 - ∣ x - 5 ∣)

- \frac{x - 5}{∣ x - 5 ∣}

Solution steps

\frac{d}{d x} (5 - ∣ x - 5 ∣)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (5) - \frac{d}{d x} (∣ x - 5 ∣)

\frac{d}{d x} (5) = 0

\frac{d}{d x} (∣ x - 5 ∣) = \frac{x - 5}{∣ x - 5 ∣}

= 0 - \frac{x - 5}{∣ x - 5 ∣}

Simplify

= - \frac{x - 5}{∣ x - 5 ∣}

\frac{\partial}{\partial o} (r cos (o))

\frac{\partial}{\partial x} (- 36 y sin (9 x))

\frac{\partial}{\partial x} (3 x - 2 y^{4})

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

x \to - 5 - lim (\frac{x + 3}{x + 5})

What is the derivative of 5-|x-5| ?
The derivative of 5-|x-5| is -(x-5)/(|x-5|)
What is the first derivative of 5-|x-5| ?
The first derivative of 5-|x-5| is -(x-5)/(|x-5|)