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

The derivative of ln(sqrt((3x/(x+2)))) is 1/(x(x+2))

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

The first derivative of ln(sqrt((3x/(x+2)))) is 1/(x(x+2))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d}{d x} (32 cos (2 x))

x \to - 2 lim (3)

\frac{d}{d x} (8 sec^{2} (x))

\int_{1}^{2} x e^{x^{2}} d x

\int - 2 tan (2 y) d y

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