en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of xln(2x+1)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d x}{d x} = 1

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

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

Simplify

1 \cdot ln (2 x + 1) + \frac{2}{2 x + 1} x : ln (2 x + 1) + \frac{2 x}{2 x + 1}

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

Popular Examples

derivative of 1/3 cos(3x)

\frac{d}{d x} (\frac{1}{3} cos (3 x))

derivative of (2x-4^4(x^2+x+1)^5)

\frac{d}{d x} ((2 x - 4)^{4} (x^{2} + x + 1)^{5})

area x^2(x-4),[-1,5]area

x^{2} (x - 4), [- 1, 5]

integral of ((5x+3))/((x^2+4x+7))

\int \frac{( 5 x + 3 )}{( x ^{2} + 4 x + 7 )} d x

derivative of (5x-1^2)

\frac{d}{d x} ((5 x - 1)^{2})

Frequently Asked Questions (FAQ)

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