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

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

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

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

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

\frac{2 x}{∣ x ∣}

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= 2 \cdot \frac{\frac{d}{d x} ( x ^{2} ) ∣ x ∣ - \frac{d}{d x} ( ∣ x ∣ ) x ^{2}}{∣ x ∣ ^{2}}

\frac{d}{d x} (x^{2}) = 2 x

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

= 2 \cdot \frac{2 x ∣ x ∣ - \frac{x}{∣ x ∣} x ^{2}}{∣ x ∣ ^{2}}

Simplify

2 \cdot \frac{2 x ∣ x ∣ - \frac{x}{∣ x ∣} x ^{2}}{∣ x ∣ ^{2}} : \frac{2 x}{∣ x ∣}

= \frac{2 x}{∣ x ∣}

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

y = x^{3} - 2 x + 2 (4.58)

x^{3} + x^{2} - 6 x, - x^{2} + 2 x

\frac{d}{d x} (5 x^{- 2} + 500)

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