en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of (x+3ln(4x+2))

Solution

\frac{d}{d x} ((x + 3) ln (4 x + 2))

Solution

ln (4 x + 2) + \frac{2 ( x + 3 )}{2 x + 1}

Solution steps

\frac{d}{d x} ((x + 3) ln (4 x + 2))

Apply the Product Rule:

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

f = x + 3, g = ln (4 x + 2)

= \frac{d}{d x} (x + 3) ln (4 x + 2) + \frac{d}{d x} (ln (4 x + 2)) (x + 3)

\frac{d}{d x} (x + 3) = 1

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

= 1 \cdot ln (4 x + 2) + \frac{2}{2 x + 1} (x + 3)

Simplify

1 \cdot ln (4 x + 2) + \frac{2}{2 x + 1} (x + 3) : ln (4 x + 2) + \frac{2 ( x + 3 )}{2 x + 1}

= ln (4 x + 2) + \frac{2 ( x + 3 )}{2 x + 1}

Popular Examples

simplify (x^2}{100}+8+\frac{20)/x simplify

\frac{x ^{2}}{100} + 8 + \frac{20}{x}

integral of (1.05)/(1+100e^{-0.285x)}

\int \frac{1.05}{1 + 100 e ^{- 0.285 x}} d x

sum from n=0 to infinity of 4/(5^n)

n = 0 \sum \infty \frac{4}{5 ^{n}}

integral from 0 to pi/3 of x^2cos(3x)

\int_{0}^{\frac{π}{3}} x^{2} cos (3 x) d x

integral of (1/y-2xsin(y))

\int (\frac{1}{y} - 2 x sin (y)) d y

Frequently Asked Questions (FAQ)

What is the derivative of (x+3ln(4x+2)) ?
The derivative of (x+3ln(4x+2)) is ln(4x+2)+(2(x+3))/(2x+1)
What is the first derivative of (x+3ln(4x+2)) ?
The first derivative of (x+3ln(4x+2)) is ln(4x+2)+(2(x+3))/(2x+1)