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Popular Calculus >

derivative of ln(x^3-27x-5)

Solution

\frac{d}{d x} (ln (x^{3} - 27 x - 5))

Solution

\frac{3 x ^{2} - 27}{x ^{3} - 27 x - 5}

Solution steps

\frac{d}{d x} (ln (x^{3} - 27 x - 5))

Apply the chain rule:

\frac{1}{x ^{3} - 27 x - 5} \frac{d}{d x} (x^{3} - 27 x - 5)

= \frac{1}{x ^{3} - 27 x - 5} \frac{d}{d x} (x^{3} - 27 x - 5)

\frac{d}{d x} (x^{3} - 27 x - 5) = 3 x^{2} - 27

= \frac{1}{x ^{3} - 27 x - 5} (3 x^{2} - 27)

Simplify

\frac{1}{x ^{3} - 27 x - 5} (3 x^{2} - 27) : \frac{3 x ^{2} - 27}{x ^{3} - 27 x - 5}

= \frac{3 x ^{2} - 27}{x ^{3} - 27 x - 5}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of ln(x^3-27x-5) ?
The derivative of ln(x^3-27x-5) is (3x^2-27)/(x^3-27x-5)
What is the first derivative of ln(x^3-27x-5) ?
The first derivative of ln(x^3-27x-5) is (3x^2-27)/(x^3-27x-5)