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

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

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

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

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Popular >

\frac{d}{d x} (\frac{x ∣ x ∣}{2})

\frac{x ^{2}}{∣ x ∣}

Solution steps

\frac{d}{d x} (\frac{x ∣ x ∣}{2})

Take the constant out:

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

= \frac{1}{2} \frac{d}{d x} (x ∣ x ∣)

Apply the Product Rule:

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

f = x, g = ∣ x ∣

= \frac{1}{2} (\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 ∣}

= \frac{1}{2} (1 \cdot ∣ x ∣ + \frac{x}{∣ x ∣} x)

Simplify

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

= \frac{x ^{2}}{∣ x ∣}

\frac{60}{x}

\int \frac{1}{9 - x ^{2}} d x

\int e^{- k N x} d x

y = A x^{2} + B e^{2 x}

y^{^{'}} = 2 x y, y (0) = 1

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