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

The derivative of ln(((2x+1^3)/((3x-1)^4))) is (6(-x-3))/((2x+1)(3x-1))

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

The first derivative of ln(((2x+1^3)/((3x-1)^4))) is (6(-x-3))/((2x+1)(3x-1))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

\frac{6 ( - x - 3 )}{( 2 x + 1 ) ( 3 x - 1 )}

Solution steps

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

Apply the chain rule:

\frac{1}{\frac{( 2 x + 1 ) ^{3}}{( 3 x - 1 ) ^{4}}} \frac{d}{d x} (\frac{( 2 x + 1 ) ^{3}}{( 3 x - 1 ) ^{4}})

= \frac{1}{\frac{( 2 x + 1 ) ^{3}}{( 3 x - 1 ) ^{4}}} \frac{d}{d x} (\frac{( 2 x + 1 ) ^{3}}{( 3 x - 1 ) ^{4}})

\frac{d}{d x} (\frac{( 2 x + 1 ) ^{3}}{( 3 x - 1 ) ^{4}}) = \frac{6 ( 2 x + 1 ) ^{2} ( - x - 3 )}{( 3 x - 1 ) ^{5}}

= \frac{1}{\frac{( 2 x + 1 ) ^{3}}{( 3 x - 1 ) ^{4}}} \cdot \frac{6 ( 2 x + 1 ) ^{2} ( - x - 3 )}{( 3 x - 1 ) ^{5}}

Simplify

\frac{1}{\frac{( 2 x + 1 ) ^{3}}{( 3 x - 1 ) ^{4}}} \cdot \frac{6 ( 2 x + 1 ) ^{2} ( - x - 3 )}{( 3 x - 1 ) ^{5}} : \frac{6 ( - x - 3 )}{( 2 x + 1 ) ( 3 x - 1 )}

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

What is the derivative of ln(((2x+1^3)/((3x-1)^4))) ?
The derivative of ln(((2x+1^3)/((3x-1)^4))) is (6(-x-3))/((2x+1)(3x-1))
What is the first derivative of ln(((2x+1^3)/((3x-1)^4))) ?
The first derivative of ln(((2x+1^3)/((3x-1)^4))) is (6(-x-3))/((2x+1)(3x-1))