What is the derivative of 4x|x| ?

The derivative of 4x|x| is (8x^2)/(|x|)

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

The first derivative of 4x|x| is (8x^2)/(|x|)

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derivative of

4 x ∣ x ∣

\frac{8 x ^{2}}{∣ x ∣}

Solution steps

\frac{d}{d x} (4 x ∣ x ∣)

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 4 \frac{d}{d x} (x ∣ x ∣)

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = ∣ x ∣

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

\frac{d x}{d x} = 1

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

= 4 (1 \cdot ∣ x ∣ + \frac{x}{∣ x ∣} x)

Simplify

4 (1 \cdot ∣ x ∣ + \frac{x}{∣ x ∣} x) : \frac{8 x ^{2}}{∣ x ∣}

= \frac{8 x ^{2}}{∣ x ∣}

3 x - cos (x) - 1

\frac{d}{d t} (10 + 2 t)

y = 2 e^{3}

(x^{2} + 3)^{4} (x + 1)

(2 x + 5)^{\frac{1}{3}}

What is the derivative of 4x|x| ?
The derivative of 4x|x| is (8x^2)/(|x|)
What is the first derivative of 4x|x| ?
The first derivative of 4x|x| is (8x^2)/(|x|)