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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

2 sin (t) \cdot cos (t)

y^{^{'}} = (x + y - 4)^{2}

x \to 1 lim (cos (π \cdot x))

\int_{2}^{\infty} x e^{- x^{2}} d x

\frac{d}{d x} (4 - x)

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