What is the derivative of ln(sqrt(x^2-1)) ?

The derivative of ln(sqrt(x^2-1)) is x/(x^2-1)

What is the first derivative of ln(sqrt(x^2-1)) ?

The first derivative of ln(sqrt(x^2-1)) is x/(x^2-1)

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

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

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

Simplify

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

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

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\int \frac{1}{x 4 - x ^{2}} d x

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

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