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Popular Calculus >

derivative of ln((x^2-81/k))

Solution

\frac{d}{d x} (ln (\frac{x ^{2} - 81}{k}))

Solution

\frac{2 x}{x ^{2} - 81}

Solution steps

\frac{d}{d x} (ln (\frac{x ^{2} - 81}{k}))

Apply the chain rule:

\frac{1}{\frac{x ^{2} - 81}{k}} \frac{d}{d x} (\frac{x ^{2} - 81}{k})

= \frac{1}{\frac{x ^{2} - 81}{k}} \frac{d}{d x} (\frac{x ^{2} - 81}{k})

\frac{d}{d x} (\frac{x ^{2} - 81}{k}) = \frac{2 x}{k}

= \frac{1}{\frac{x ^{2} - 81}{k}} \cdot \frac{2 x}{k}

Simplify

\frac{1}{\frac{x ^{2} - 81}{k}} \cdot \frac{2 x}{k} : \frac{2 x}{x ^{2} - 81}

= \frac{2 x}{x ^{2} - 81}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of ln((x^2-81/k)) ?
The derivative of ln((x^2-81/k)) is (2x)/(x^2-81)
What is the first derivative of ln((x^2-81/k)) ?
The first derivative of ln((x^2-81/k)) is (2x)/(x^2-81)