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Popular >

derivative of ln(6x^2+3x)

Solution

\frac{d}{d x} (ln (6 x^{2} + 3 x))

Solution

\frac{4 x + 1}{x ( 2 x + 1 )}

Solution steps

\frac{d}{d x} (ln (6 x^{2} + 3 x))

Apply the chain rule:

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

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

\frac{d}{d x} (6 x^{2} + 3 x) = 12 x + 3

= \frac{1}{6 x ^{2} + 3 x} (12 x + 3)

Simplify

\frac{1}{6 x ^{2} + 3 x} (12 x + 3) : \frac{4 x + 1}{x ( 2 x + 1 )}

= \frac{4 x + 1}{x ( 2 x + 1 )}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of ln(6x^2+3x) ?
The derivative of ln(6x^2+3x) is (4x+1)/(x(2x+1))
What is the first derivative of ln(6x^2+3x) ?
The first derivative of ln(6x^2+3x) is (4x+1)/(x(2x+1))