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Popular >

derivative of ln(5x^3+2x)

Solution

\frac{d}{d x} (ln (5 x^{3} + 2 x))

Solution

\frac{15 x ^{2} + 2}{5 x ^{3} + 2 x}

Solution steps

\frac{d}{d x} (ln (5 x^{3} + 2 x))

Apply the chain rule:

\frac{1}{5 x ^{3} + 2 x} \frac{d}{d x} (5 x^{3} + 2 x)

= \frac{1}{5 x ^{3} + 2 x} \frac{d}{d x} (5 x^{3} + 2 x)

\frac{d}{d x} (5 x^{3} + 2 x) = 15 x^{2} + 2

= \frac{1}{5 x ^{3} + 2 x} (15 x^{2} + 2)

Simplify

\frac{1}{5 x ^{3} + 2 x} (15 x^{2} + 2) : \frac{15 x ^{2} + 2}{5 x ^{3} + 2 x}

= \frac{15 x ^{2} + 2}{5 x ^{3} + 2 x}

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Frequently Asked Questions (FAQ)

What is the derivative of ln(5x^3+2x) ?
The derivative of ln(5x^3+2x) is (15x^2+2)/(5x^3+2x)
What is the first derivative of ln(5x^3+2x) ?
The first derivative of ln(5x^3+2x) is (15x^2+2)/(5x^3+2x)