What is the derivative of sqrt(|X^2-1|) ?

The derivative of sqrt(|X^2-1|) is (X(X^2-1))/(|X^2-1|sqrt(|X^2-1|))

What is the first derivative of sqrt(|X^2-1|) ?

The first derivative of sqrt(|X^2-1|) is (X(X^2-1))/(|X^2-1|sqrt(|X^2-1|))

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derivative of

∣ X^{2} - 1 ∣

\frac{X ( X ^{2} - 1 )}{∣ X ^{2} - 1 ∣ ∣ X ^{2} - 1 ∣}

Solution steps

\frac{d}{d X} (∣ X^{2} - 1 ∣)

Apply the chain rule:

\frac{1}{2 ∣ X ^{2} - 1 ∣} \frac{d}{d X} (X^{2} - 1)

= \frac{1}{2 ∣ X ^{2} - 1 ∣} \frac{d}{d X} (X^{2} - 1)

\frac{d}{d X} (X^{2} - 1) = \frac{2 X ( X ^{2} - 1 )}{∣ X ^{2} - 1 ∣}

= \frac{1}{2 ∣ X ^{2} - 1 ∣} \cdot \frac{2 X ( X ^{2} - 1 )}{∣ X ^{2} - 1 ∣}

Simplify

\frac{1}{2 ∣ X ^{2} - 1 ∣} \cdot \frac{2 X ( X ^{2} - 1 )}{∣ X ^{2} - 1 ∣} : \frac{X ( X ^{2} - 1 )}{∣ X ^{2} - 1 ∣ ∣ X ^{2} - 1 ∣}

= \frac{X ( X ^{2} - 1 )}{∣ X ^{2} - 1 ∣ ∣ X ^{2} - 1 ∣}

\int e^{t y} (- 4 y - 1) d y

(4 - \frac{1}{2 x ^{2}})^{- 1}

f (x) = x^{2} - 3 x - 4, (2, - 6)

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

\frac{\partial}{\partial x} (\frac{x - 3 y}{x ^{2} + y ^{2}})

What is the derivative of sqrt(|X^2-1|) ?
The derivative of sqrt(|X^2-1|) is (X(X^2-1))/(|X^2-1|sqrt(|X^2-1|))
What is the first derivative of sqrt(|X^2-1|) ?
The first derivative of sqrt(|X^2-1|) is (X(X^2-1))/(|X^2-1|sqrt(|X^2-1|))