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Popular >

derivative of ln(xsqrt(4x-1))

Solution

\frac{d}{d x} (ln (x 4 x - 1))

Solution

\frac{6 x - 1}{x ( 4 x - 1 )}

Solution steps

\frac{d}{d x} (ln (x 4 x - 1))

Apply the chain rule:

\frac{1}{x 4 x - 1} \frac{d}{d x} (x 4 x - 1)

= \frac{1}{x 4 x - 1} \frac{d}{d x} (x 4 x - 1)

\frac{d}{d x} (x 4 x - 1) = \frac{6 x - 1}{4 x - 1}

= \frac{1}{x 4 x - 1} \cdot \frac{6 x - 1}{4 x - 1}

Simplify

\frac{1}{x 4 x - 1} \cdot \frac{6 x - 1}{4 x - 1} : \frac{6 x - 1}{x ( 4 x - 1 )}

= \frac{6 x - 1}{x ( 4 x - 1 )}

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Frequently Asked Questions (FAQ)

What is the derivative of ln(xsqrt(4x-1)) ?
The derivative of ln(xsqrt(4x-1)) is (6x-1)/(x(4x-1))
What is the first derivative of ln(xsqrt(4x-1)) ?
The first derivative of ln(xsqrt(4x-1)) is (6x-1)/(x(4x-1))