What is the derivative of ln(x^6-1) ?

The derivative of ln(x^6-1) is (6x^5)/(x^6-1)

What is the first derivative of ln(x^6-1) ?

The first derivative of ln(x^6-1) is (6x^5)/(x^6-1)

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\frac{d}{d x} (ln (x^{6} - 1))

\frac{6 x ^{5}}{x ^{6} - 1}

Solution steps

\frac{d}{d x} (ln (x^{6} - 1))

Apply the chain rule:

\frac{1}{x ^{6} - 1} \frac{d}{d x} (x^{6} - 1)

= \frac{1}{x ^{6} - 1} \frac{d}{d x} (x^{6} - 1)

\frac{d}{d x} (x^{6} - 1) = 6 x^{5}

= \frac{1}{x ^{6} - 1} \cdot 6 x^{5}

Simplify

\frac{1}{x ^{6} - 1} \cdot 6 x^{5} : \frac{6 x ^{5}}{x ^{6} - 1}

= \frac{6 x ^{5}}{x ^{6} - 1}

t an g e n t y = x^{3}, (2, 8)

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

\frac{d}{d x} ((3 x - 7)^{12})

\int \frac{x + 1}{2 x} d x

f (x) = e^{x} + ln (x)

What is the derivative of ln(x^6-1) ?
The derivative of ln(x^6-1) is (6x^5)/(x^6-1)
What is the first derivative of ln(x^6-1) ?
The first derivative of ln(x^6-1) is (6x^5)/(x^6-1)