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

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

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

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

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derivative of

y = 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}

\frac{d}{d x} (6 sin^{6} (x))

\int - 7 sin (7 x) d x

\int_{8}^{16} x 16 x - x^{2} d x

\frac{( 5 x - 25 )}{x ^{2} - 5 x}

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