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

The derivative of ((x+1/(x-3))^2) is -(8(x+1))/((x-3)^3)

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

The first derivative of ((x+1/(x-3))^2) is -(8(x+1))/((x-3)^3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

- \frac{8 ( x + 1 )}{( x - 3 ) ^{3}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

2 \cdot \frac{x + 1}{x - 3} (- \frac{4}{( x - 3 ) ^{2}}) : - \frac{8 ( x + 1 )}{( x - 3 ) ^{3}}

= - \frac{8 ( x + 1 )}{( x - 3 ) ^{3}}

What is the derivative of ((x+1/(x-3))^2) ?
The derivative of ((x+1/(x-3))^2) is -(8(x+1))/((x-3)^3)
What is the first derivative of ((x+1/(x-3))^2) ?
The first derivative of ((x+1/(x-3))^2) is -(8(x+1))/((x-3)^3)