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)

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Popular >

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

\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}

6 - 7 x

\frac{d}{d x} (sin^{12} (3 x^{4} - x))

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

3 t^{2} - 9 t

(4 x + 5)^{\frac{1}{5}}

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)