What is the derivative of ln(sqrt(x^2-14)) ?

The derivative of ln(sqrt(x^2-14)) is x/(x^2-14)

What is the first derivative of ln(sqrt(x^2-14)) ?

The first derivative of ln(sqrt(x^2-14)) is x/(x^2-14)

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\frac{d}{d x} (ln (x^{2} - 14))

\frac{x}{x ^{2} - 14}

Solution steps

\frac{d}{d x} (ln (x^{2} - 14))

Apply the chain rule:

\frac{1}{x ^{2} - 14} \frac{d}{d x} (x^{2} - 14)

= \frac{1}{x ^{2} - 14} \frac{d}{d x} (x^{2} - 14)

\frac{d}{d x} (x^{2} - 14) = \frac{x}{x ^{2} - 14}

= \frac{1}{x ^{2} - 14} \cdot \frac{x}{x ^{2} - 14}

Simplify

\frac{1}{x ^{2} - 14} \cdot \frac{x}{x ^{2} - 14} : \frac{x}{x ^{2} - 14}

= \frac{x}{x ^{2} - 14}

What is the derivative of ln(sqrt(x^2-14)) ?
The derivative of ln(sqrt(x^2-14)) is x/(x^2-14)
What is the first derivative of ln(sqrt(x^2-14)) ?
The first derivative of ln(sqrt(x^2-14)) is x/(x^2-14)