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Popular >

derivative of sqrt(|x|)

Solution

\frac{d}{d x} (∣ x ∣)

Solution

\frac{x}{2 ∣ x ∣ ∣ x ∣}

Solution steps

\frac{d}{d x} (∣ x ∣)

Apply the chain rule:

\frac{1}{2 ∣ x ∣} \frac{d}{d x} (∣ x ∣)

= \frac{1}{2 ∣ x ∣} \frac{d}{d x} (∣ x ∣)

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

= \frac{1}{2 ∣ x ∣} \cdot \frac{x}{∣ x ∣}

Simplify

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

= \frac{x}{2 ∣ x ∣ ∣ x ∣}

Graph

Popular Examples

integral from 1 to 2 of (3x-2)^2

\int_{1}^{2} (3 x - 2)^{2} d x

xy^'+y=-9xy^2,y(1)=-4

x y^{^{'}} + y = - 9 x y^{2}, y (1) = - 4

integral from 0 to pi/5 of sin^4(5x)

\int_{0}^{\frac{π}{5}} sin^{4} (5 x) d x

y^'+y= 1/(1+t^2)

y^{^{'}} + y = \frac{1}{1 + t ^{2}}

limit as x approaches 0 of x^2ln(4x^2)

x \to 0 lim (x^{2} ln (4 x^{2}))

Frequently Asked Questions (FAQ)

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