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

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

y = (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)

2 sin (π t)

f (x) = x^{4} - 2 x^{2} + 1, at x = - 2

y = 2 e^{x} cos (x), (0, 2)

\frac{d}{d x} (cos^{3} (4 x^{2}))

\frac{d}{d x} (ln (a x^{n}))

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