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Popular >

derivative of ln((x^3-4/x))

Solution

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

Solution

\frac{2 x ^{3} + 4}{x ( x ^{3} - 4 )}

Solution steps

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

Apply the chain rule:

\frac{1}{\frac{x ^{3} - 4}{x}} \frac{d}{d x} (\frac{x ^{3} - 4}{x})

= \frac{1}{\frac{x ^{3} - 4}{x}} \frac{d}{d x} (\frac{x ^{3} - 4}{x})

\frac{d}{d x} (\frac{x ^{3} - 4}{x}) = \frac{2 x ^{3} + 4}{x ^{2}}

= \frac{1}{\frac{x ^{3} - 4}{x}} \cdot \frac{2 x ^{3} + 4}{x ^{2}}

Simplify

\frac{1}{\frac{x ^{3} - 4}{x}} \cdot \frac{2 x ^{3} + 4}{x ^{2}} : \frac{2 x ^{3} + 4}{x ( x ^{3} - 4 )}

= \frac{2 x ^{3} + 4}{x ( x ^{3} - 4 )}

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Frequently Asked Questions (FAQ)

What is the derivative of ln((x^3-4/x)) ?
The derivative of ln((x^3-4/x)) is (2x^3+4)/(x(x^3-4))
What is the first derivative of ln((x^3-4/x)) ?
The first derivative of ln((x^3-4/x)) is (2x^3+4)/(x(x^3-4))