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Popular >

derivative of ln(3x^3+x+6)

Solution

\frac{d}{d x} (ln (3 x^{3} + x + 6))

Solution

\frac{9 x ^{2} + 1}{3 x ^{3} + x + 6}

Solution steps

\frac{d}{d x} (ln (3 x^{3} + x + 6))

Apply the chain rule:

\frac{1}{3 x ^{3} + x + 6} \frac{d}{d x} (3 x^{3} + x + 6)

= \frac{1}{3 x ^{3} + x + 6} \frac{d}{d x} (3 x^{3} + x + 6)

\frac{d}{d x} (3 x^{3} + x + 6) = 9 x^{2} + 1

= \frac{1}{3 x ^{3} + x + 6} (9 x^{2} + 1)

Simplify

\frac{1}{3 x ^{3} + x + 6} (9 x^{2} + 1) : \frac{9 x ^{2} + 1}{3 x ^{3} + x + 6}

= \frac{9 x ^{2} + 1}{3 x ^{3} + x + 6}

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Frequently Asked Questions (FAQ)

What is the derivative of ln(3x^3+x+6) ?
The derivative of ln(3x^3+x+6) is (9x^2+1)/(3x^3+x+6)
What is the first derivative of ln(3x^3+x+6) ?
The first derivative of ln(3x^3+x+6) is (9x^2+1)/(3x^3+x+6)