What is the derivative of ((3x-4/(5x+2))^{-5}) ?

The derivative of ((3x-4/(5x+2))^{-5}) is -(130(5x+2)^4)/((3x-4)^6)

What is the first derivative of ((3x-4/(5x+2))^{-5}) ?

The first derivative of ((3x-4/(5x+2))^{-5}) is -(130(5x+2)^4)/((3x-4)^6)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

- \frac{130 ( 5 x + 2 ) ^{4}}{( 3 x - 4 ) ^{6}}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{3 x - 4}{5 x + 2}) = \frac{26}{( 5 x + 2 ) ^{2}}

= - \frac{5}{( \frac{3 x - 4}{5 x + 2} ) ^{6}} \cdot \frac{26}{( 5 x + 2 ) ^{2}}

Simplify

- \frac{5}{( \frac{3 x - 4}{5 x + 2} ) ^{6}} \cdot \frac{26}{( 5 x + 2 ) ^{2}} : - \frac{130 ( 5 x + 2 ) ^{4}}{( 3 x - 4 ) ^{6}}

= - \frac{130 ( 5 x + 2 ) ^{4}}{( 3 x - 4 ) ^{6}}

ln (\frac{x}{4 x ^{2} + x})

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

\int_{0}^{1} e^{- 3 x} d x

\frac{\partial}{\partial x} (\frac{1}{y} - 2 x sin (y))

\frac{d}{d x} (\frac{( e ^{x} - 1 )}{x})

What is the derivative of ((3x-4/(5x+2))^{-5}) ?
The derivative of ((3x-4/(5x+2))^{-5}) is -(130(5x+2)^4)/((3x-4)^6)
What is the first derivative of ((3x-4/(5x+2))^{-5}) ?
The first derivative of ((3x-4/(5x+2))^{-5}) is -(130(5x+2)^4)/((3x-4)^6)