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Popular >

derivative of x|x|

Solution

derivative of

x ∣ x ∣

Solution

\frac{2 x ^{2}}{∣ x ∣}

Solution steps

\frac{d}{d x} (x ∣ x ∣)

Apply the Product Rule:

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

f = x, g = ∣ x ∣

= \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 ∣}

= 1 \cdot ∣ x ∣ + \frac{x}{∣ x ∣} x

Simplify

1 \cdot ∣ x ∣ + \frac{x}{∣ x ∣} x : \frac{2 x ^{2}}{∣ x ∣}

= \frac{2 x ^{2}}{∣ x ∣}

Popular Examples

integral of (3x)/1

\int \frac{3 x}{1} d x

sum from n=1 to infinity of 2n+1

n = 1 \sum \infty 2 n + 1

limit as x approaches 1/2 of xtan(pi)x

x \to \frac{1}{2} lim (x tan (π) x)

limit as x approaches 3/2 of (8x^3-27)/(2x-3)

x \to \frac{3}{2} lim (\frac{8 x ^{3} - 27}{2 x - 3})

derivative of x^2e^x+2xe^x

\frac{d}{d x} (x^{2} e^{x} + 2 x e^{x})

Frequently Asked Questions (FAQ)

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