en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

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

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

\frac{1}{\frac{2 x}{x + 3}} \frac{d}{d x} (\frac{2 x}{x + 3})

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

\frac{d}{d x} (\frac{2 x}{x + 3}) = \frac{6}{( x + 3 ) ^{2}}

= \frac{1}{\frac{2 x}{x + 3}} \cdot \frac{6}{( x + 3 ) ^{2}}

Simplify

\frac{1}{\frac{2 x}{x + 3}} \cdot \frac{6}{( x + 3 ) ^{2}} : \frac{3}{x ( x + 3 )}

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

Graph

Popular Examples

integral of 1-2cos(x)

\int 1 - 2 cos (x) d x

derivative of (13e^{6x})/(x+5)

d er i v a t i v e \frac{13 e ^{6 x}}{x + 5}

integral of (4x+1)^2

\int (4 x + 1)^{2} d x

integral of 5/(x+4)

\int \frac{5}{x + 4} d x

derivative of f(x)=(3t-1)/(sqrt(t)-2)

d er i v a t i v e f (x) = \frac{3 t - 1}{t - 2}

Frequently Asked Questions (FAQ)

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