What is the derivative of f(x)=((x+1)/(x-1))^7 ?

The derivative of f(x)=((x+1)/(x-1))^7 is -(14(x+1)^6)/((x-1)^8)

What is the first derivative of f(x)=((x+1)/(x-1))^7 ?

The first derivative of f(x)=((x+1)/(x-1))^7 is -(14(x+1)^6)/((x-1)^8)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

f (x) = (\frac{x + 1}{x - 1})^{7}

- \frac{14 ( x + 1 ) ^{6}}{( x - 1 ) ^{8}}

Solution steps

\frac{d}{d x} ((\frac{x + 1}{x - 1})^{7})

Apply the chain rule:

7 (\frac{x + 1}{x - 1})^{6} \frac{d}{d x} (\frac{x + 1}{x - 1})

= 7 (\frac{x + 1}{x - 1})^{6} \frac{d}{d x} (\frac{x + 1}{x - 1})

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

= 7 (\frac{x + 1}{x - 1})^{6} (- \frac{2}{( x - 1 ) ^{2}})

Simplify

7 (\frac{x + 1}{x - 1})^{6} (- \frac{2}{( x - 1 ) ^{2}}) : - \frac{14 ( x + 1 ) ^{6}}{( x - 1 ) ^{8}}

= - \frac{14 ( x + 1 ) ^{6}}{( x - 1 ) ^{8}}

\frac{d}{d x} (lo g_{4} (cos (2 x)))

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

\int r^{2} + z^{2} d z

\frac{d}{d t} (2 sin (t))

f (x) = \frac{x ^{2}}{3}

What is the derivative of f(x)=((x+1)/(x-1))^7 ?
The derivative of f(x)=((x+1)/(x-1))^7 is -(14(x+1)^6)/((x-1)^8)
What is the first derivative of f(x)=((x+1)/(x-1))^7 ?
The first derivative of f(x)=((x+1)/(x-1))^7 is -(14(x+1)^6)/((x-1)^8)