What is the derivative of ln(2x-sqrt(x)) ?

The derivative of ln(2x-sqrt(x)) is (4sqrt(x)-1)/(2sqrt(x)(2x-\sqrt{x))}

What is the first derivative of ln(2x-sqrt(x)) ?

The first derivative of ln(2x-sqrt(x)) is (4sqrt(x)-1)/(2sqrt(x)(2x-\sqrt{x))}

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\frac{d}{d x} (ln (2 x - x))

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

Solution steps

\frac{d}{d x} (ln (2 x - x))

Apply the chain rule:

\frac{1}{2 x - x} \frac{d}{d x} (2 x - x)

= \frac{1}{2 x - x} \frac{d}{d x} (2 x - x)

\frac{d}{d x} (2 x - x) = 2 - \frac{1}{2 x}

= \frac{1}{2 x - x} (2 - \frac{1}{2 x})

Simplify

\frac{1}{2 x - x} (2 - \frac{1}{2 x}) : \frac{4 x - 1}{2 x ( 2 x - x )}

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

What is the derivative of ln(2x-sqrt(x)) ?
The derivative of ln(2x-sqrt(x)) is (4sqrt(x)-1)/(2sqrt(x)(2x-\sqrt{x))}
What is the first derivative of ln(2x-sqrt(x)) ?
The first derivative of ln(2x-sqrt(x)) is (4sqrt(x)-1)/(2sqrt(x)(2x-\sqrt{x))}