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Popular Calculus >

derivative of ln|x^2-1|

Solution

\frac{d}{d x} (ln x^{2} - 1)

Solution

\frac{2 x}{x ^{2} - 1}

Solution steps

\frac{d}{d x} (ln x^{2} - 1)

Apply the chain rule:

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

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

Simplify

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

= \frac{2 x}{x ^{2} - 1}

Graph

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\int \frac{5}{1 + 9 x ^{2}} d x

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Frequently Asked Questions (FAQ)

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