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Popular >

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

Solution

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

Solution

\frac{5 x ^{2} - 9}{x ( x ^{2} - 3 )}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (x^{5} - 3 x^{3}) = 5 x^{4} - 9 x^{2}

= \frac{1}{x ^{5} - 3 x ^{3}} (5 x^{4} - 9 x^{2})

Simplify

\frac{1}{x ^{5} - 3 x ^{3}} (5 x^{4} - 9 x^{2}) : \frac{5 x ^{2} - 9}{x ( x ^{2} - 3 )}

= \frac{5 x ^{2} - 9}{x ( x ^{2} - 3 )}

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n = 0 \sum \infty \frac{1}{6 ^{n}}

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\frac{d}{d t} (sin (t^{3}))

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\int \frac{x ^{3} + 3 x ^{2} - 5 x - 1}{x ^{2} - x} d x

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Frequently Asked Questions (FAQ)

What is the derivative of ln(x^5-3x^3) ?
The derivative of ln(x^5-3x^3) is (5x^2-9)/(x(x^2-3))
What is the first derivative of ln(x^5-3x^3) ?
The first derivative of ln(x^5-3x^3) is (5x^2-9)/(x(x^2-3))