What is the derivative of ln((x^2-7/x)) ?

The derivative of ln((x^2-7/x)) is (x^2+7)/(x(x^2-7))

What is the first derivative of ln((x^2-7/x)) ?

The first derivative of ln((x^2-7/x)) is (x^2+7)/(x(x^2-7))

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\frac{d}{d x} (ln (\frac{x ^{2} - 7}{x}))

\frac{x ^{2} + 7}{x ( x ^{2} - 7 )}

Solution steps

\frac{d}{d x} (ln (\frac{x ^{2} - 7}{x}))

Apply the chain rule:

\frac{1}{\frac{x ^{2} - 7}{x}} \frac{d}{d x} (\frac{x ^{2} - 7}{x})

= \frac{1}{\frac{x ^{2} - 7}{x}} \frac{d}{d x} (\frac{x ^{2} - 7}{x})

\frac{d}{d x} (\frac{x ^{2} - 7}{x}) = \frac{x ^{2} + 7}{x ^{2}}

= \frac{1}{\frac{x ^{2} - 7}{x}} \cdot \frac{x ^{2} + 7}{x ^{2}}

Simplify

\frac{1}{\frac{x ^{2} - 7}{x}} \cdot \frac{x ^{2} + 7}{x ^{2}} : \frac{x ^{2} + 7}{x ( x ^{2} - 7 )}

= \frac{x ^{2} + 7}{x ( x ^{2} - 7 )}

What is the derivative of ln((x^2-7/x)) ?
The derivative of ln((x^2-7/x)) is (x^2+7)/(x(x^2-7))
What is the first derivative of ln((x^2-7/x)) ?
The first derivative of ln((x^2-7/x)) is (x^2+7)/(x(x^2-7))