What is the derivative of (2x-1^2ln(2x-1)) ?

The derivative of (2x-1^2ln(2x-1)) is 4ln(2x-1)(2x-1)+2(2x-1)

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

The first derivative of (2x-1^2ln(2x-1)) is 4ln(2x-1)(2x-1)+2(2x-1)

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

4 ln (2 x - 1) (2 x - 1) + 2 (2 x - 1)

Solution steps

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

Apply the Product Rule:

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

f = (2 x - 1)^{2}, g = ln (2 x - 1)

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

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

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

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

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

= 4 ln (2 x - 1) (2 x - 1) + 2 (2 x - 1)

f (x) = (x) (3 x - 2)

\frac{d y}{d t} = 3 y + y^{6}, y (0) = 1

sin (t - 2 π)

\frac{d y}{d x} (x^{2} + 4) = x y

\int 22 d x

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