What is the derivative of 2sqrt(x^2) ?

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

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

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

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

\frac{2 x}{∣ x ∣}

Solution steps

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

Take the constant out:

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

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

Apply radical rule:

a^{2} = ∣ a ∣

= 2 \frac{d}{d x} (∣ x ∣)

Apply the common derivative:

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

= 2 \cdot \frac{x}{∣ x ∣}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{2 x}{∣ x ∣}

3 x + 5

\frac{d y}{d t} = 4 y (1 - y)

\int_{1}^{2} \frac{2}{x ^{3} + x} d x

e^{3 t}

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