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

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

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

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

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derivative of

y = 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 \to - 3 lim (5 x^{2} + 2 x)

\int \frac{1 + x}{1 - 3 x} d x

x \to 3 lim (\frac{x - 2}{x - 3})

\int \frac{3}{4 ( 4 - 3 x ) ^{7}} d x

4 y^{^{''}} + 9 y = 0

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