What is the derivative of (ln(x))/(3ln(x)+1) ?

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

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

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Simplify

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

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

- 3 x^{\frac{3}{2}}

\frac{d}{d x} (\frac{6}{( 3 - 4 x ) ^{5}})

x y^{2}

x \to 2 lim (\frac{sin ( 4 x - 8 )}{3 x - 6})

\frac{d}{d x} (\frac{( e ^{x} )}{x})

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