What is the derivative of ln(x^3-1/x) ?

The derivative of ln(x^3-1/x) is (3x^4+1)/(x(x^4-1))

What is the first derivative of ln(x^3-1/x) ?

The first derivative of ln(x^3-1/x) is (3x^4+1)/(x(x^4-1))

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

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (x^{3} - \frac{1}{x}) = 3 x^{2} + \frac{1}{x ^{2}}

= \frac{1}{x ^{3} - \frac{1}{x}} (3 x^{2} + \frac{1}{x ^{2}})

Simplify

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

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

What is the derivative of ln(x^3-1/x) ?
The derivative of ln(x^3-1/x) is (3x^4+1)/(x(x^4-1))
What is the first derivative of ln(x^3-1/x) ?
The first derivative of ln(x^3-1/x) is (3x^4+1)/(x(x^4-1))