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

The derivative of ((2x+1/(3x-1))^4) is -(20(2x+1)^3)/((3x-1)^5)

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

The first derivative of ((2x+1/(3x-1))^4) is -(20(2x+1)^3)/((3x-1)^5)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

- \frac{20 ( 2 x + 1 ) ^{3}}{( 3 x - 1 ) ^{5}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

4 (\frac{2 x + 1}{3 x - 1})^{3} (- \frac{5}{( 3 x - 1 ) ^{2}}) : - \frac{20 ( 2 x + 1 ) ^{3}}{( 3 x - 1 ) ^{5}}

= - \frac{20 ( 2 x + 1 ) ^{3}}{( 3 x - 1 ) ^{5}}

What is the derivative of ((2x+1/(3x-1))^4) ?
The derivative of ((2x+1/(3x-1))^4) is -(20(2x+1)^3)/((3x-1)^5)
What is the first derivative of ((2x+1/(3x-1))^4) ?
The first derivative of ((2x+1/(3x-1))^4) is -(20(2x+1)^3)/((3x-1)^5)