What is the derivative of f(x)=((x+7)/(x-7))^5 ?

The derivative of f(x)=((x+7)/(x-7))^5 is -(70(x+7)^4)/((x-7)^6)

What is the first derivative of f(x)=((x+7)/(x-7))^5 ?

The first derivative of f(x)=((x+7)/(x-7))^5 is -(70(x+7)^4)/((x-7)^6)

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 + 7}{x - 7})^{5}

- \frac{70 ( x + 7 ) ^{4}}{( x - 7 ) ^{6}}

Solution steps

\frac{d}{d x} ((\frac{x + 7}{x - 7})^{5})

Apply the chain rule:

5 (\frac{x + 7}{x - 7})^{4} \frac{d}{d x} (\frac{x + 7}{x - 7})

= 5 (\frac{x + 7}{x - 7})^{4} \frac{d}{d x} (\frac{x + 7}{x - 7})

\frac{d}{d x} (\frac{x + 7}{x - 7}) = - \frac{14}{( x - 7 ) ^{2}}

= 5 (\frac{x + 7}{x - 7})^{4} (- \frac{14}{( x - 7 ) ^{2}})

Simplify

5 (\frac{x + 7}{x - 7})^{4} (- \frac{14}{( x - 7 ) ^{2}}) : - \frac{70 ( x + 7 ) ^{4}}{( x - 7 ) ^{6}}

= - \frac{70 ( x + 7 ) ^{4}}{( x - 7 ) ^{6}}

x^{2} - 1, - x + 2, x = 0, x = 1

\int \frac{6 + x + x}{x} d x

\int_{1}^{2} (2 - x) d x

\int sin (π x) - cos (π x) d x

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

What is the derivative of f(x)=((x+7)/(x-7))^5 ?
The derivative of f(x)=((x+7)/(x-7))^5 is -(70(x+7)^4)/((x-7)^6)
What is the first derivative of f(x)=((x+7)/(x-7))^5 ?
The first derivative of f(x)=((x+7)/(x-7))^5 is -(70(x+7)^4)/((x-7)^6)