What is the derivative of |x|^a ?

The derivative of |x|^a is ax|x|^{a-2}

What is the first derivative of |x|^a ?

The first derivative of |x|^a is ax|x|^{a-2}

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\frac{d}{d x} (∣ x ∣^{a})

a x ∣ x ∣^{a - 2}

Solution steps

\frac{d}{d x} (∣ x ∣^{a})

Apply the chain rule:

a ∣ x ∣^{a - 1} \frac{d}{d x} (∣ x ∣)

= a ∣ x ∣^{a - 1} \frac{d}{d x} (∣ x ∣)

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

= a ∣ x ∣^{a - 1} \frac{x}{∣ x ∣}

Simplify

a ∣ x ∣^{a - 1} \frac{x}{∣ x ∣} : a x ∣ x ∣^{a - 2}

= a x ∣ x ∣^{a - 2}

\int \frac{1}{x ^{2} 36 x ^{2} - 1} d x

x^{s i n (x)}

f (x) = \frac{3 x}{( x + 1 ) ^{2}}, at x = 0

f (x) = \frac{1}{x ^{2} + 1}

\frac{d}{d x} (4 sin^{3} (x))

What is the derivative of |x|^a ?
The derivative of |x|^a is ax|x|^{a-2}
What is the first derivative of |x|^a ?
The first derivative of |x|^a is ax|x|^{a-2}