What is the derivative of y=(1-x/7)^{-7} ?

The derivative of y=(1-x/7)^{-7} is (5764801)/((7-x)^8)

What is the first derivative of y=(1-x/7)^{-7} ?

The first derivative of y=(1-x/7)^{-7} is (5764801)/((7-x)^8)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

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

\frac{5764801}{( 7 - x ) ^{8}}

Solution steps

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

Apply the chain rule:

- \frac{7}{( 1 - \frac{x}{7} ) ^{8}} \frac{d}{d x} (1 - \frac{x}{7})

= - \frac{7}{( 1 - \frac{x}{7} ) ^{8}} \frac{d}{d x} (1 - \frac{x}{7})

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

= - \frac{7}{( 1 - \frac{x}{7} ) ^{8}} (- \frac{1}{7})

Simplify

- \frac{7}{( 1 - \frac{x}{7} ) ^{8}} (- \frac{1}{7}) : \frac{5764801}{( 7 - x ) ^{8}}

= \frac{5764801}{( 7 - x ) ^{8}}

What is the derivative of y=(1-x/7)^{-7} ?
The derivative of y=(1-x/7)^{-7} is (5764801)/((7-x)^8)
What is the first derivative of y=(1-x/7)^{-7} ?
The first derivative of y=(1-x/7)^{-7} is (5764801)/((7-x)^8)