en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

\frac{1}{3 x + 4} \frac{d}{d x} (3 x + 4)

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

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

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

Simplify

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

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

Popular Examples

limit as x approaches 6+of xsqrt(6-x)

x \to 6 + lim (x 6 - x)

limit as x approaches 0 of (x)sin(1/x)

x \to 0 lim ((x) sin (\frac{1}{x}))

limit as x approaches-7 of (x^2-3)/(7-x)

x \to - 7 lim (\frac{x ^{2} - 3}{7 - x})

derivative of 8(x-1/x)^3 derivative of

8 (x - \frac{1}{x})^{3}

integral of 6x^2-8x+3

\int 6 x^{2} - 8 x + 3 d x

Frequently Asked Questions (FAQ)

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