What is the derivative of 4-|x| ?

The derivative of 4-|x| is -x/(|x|)

What is the first derivative of 4-|x| ?

The first derivative of 4-|x| is -x/(|x|)

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\frac{d}{d x} (4 - ∣ x ∣)

- \frac{x}{∣ x ∣}

Solution steps

\frac{d}{d x} (4 - ∣ x ∣)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (4) - \frac{d}{d x} (∣ x ∣)

\frac{d}{d x} (4) = 0

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

= 0 - \frac{x}{∣ x ∣}

Simplify

= - \frac{x}{∣ x ∣}

\int \frac{e ^{3 x}}{( 1 - 2 e ^{3 x} ) ^{2}} d x

\frac{d}{d x} (1 - (1 + x) e^{- x})

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

f (x) = x^{4} - 2 x^{2} + 1, at x = 2

\int_{0}^{π} sin (x) sin (3 x) d x

What is the derivative of 4-|x| ?
The derivative of 4-|x| is -x/(|x|)
What is the first derivative of 4-|x| ?
The first derivative of 4-|x| is -x/(|x|)