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Popular >

derivative of (2x-1)ln(2x-1)

Solution

derivative of

(2 x - 1) ln (2 x - 1)

Solution

2 ln (2 x - 1) + 2

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 2 x - 1, g = ln (2 x - 1)

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

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

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

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

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

= 2 ln (2 x - 1) + 2

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of (2x-1)ln(2x-1) ?
The derivative of (2x-1)ln(2x-1) is 2ln(2x-1)+2
What is the first derivative of (2x-1)ln(2x-1) ?
The first derivative of (2x-1)ln(2x-1) is 2ln(2x-1)+2