What is the derivative of ln(sqrt(x^2-9)) ?

The derivative of ln(sqrt(x^2-9)) is x/(x^2-9)

What is the first derivative of ln(sqrt(x^2-9)) ?

The first derivative of ln(sqrt(x^2-9)) is x/(x^2-9)

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\frac{d}{d x} (ln (x^{2} - 9))

\frac{x}{x ^{2} - 9}

Solution steps

\frac{d}{d x} (ln (x^{2} - 9))

Apply the chain rule:

\frac{1}{x ^{2} - 9} \frac{d}{d x} (x^{2} - 9)

= \frac{1}{x ^{2} - 9} \frac{d}{d x} (x^{2} - 9)

\frac{d}{d x} (x^{2} - 9) = \frac{x}{x ^{2} - 9}

= \frac{1}{x ^{2} - 9} \cdot \frac{x}{x ^{2} - 9}

Simplify

\frac{1}{x ^{2} - 9} \cdot \frac{x}{x ^{2} - 9} : \frac{x}{x ^{2} - 9}

= \frac{x}{x ^{2} - 9}

x^{2} + (\frac{1}{2} x - 5)^{2}

f (x) = 6 x sin (x)

\frac{d y}{d x} = x x - 9

y = 3 - x, y = - 3 - x, y = x - 1

What is the derivative of ln(sqrt(x^2-9)) ?
The derivative of ln(sqrt(x^2-9)) is x/(x^2-9)
What is the first derivative of ln(sqrt(x^2-9)) ?
The first derivative of ln(sqrt(x^2-9)) is x/(x^2-9)