What is the derivative of 6/((1-x)^3) ?

The derivative of 6/((1-x)^3) is (18)/((1-x)^4)

What is the first derivative of 6/((1-x)^3) ?

The first derivative of 6/((1-x)^3) is (18)/((1-x)^4)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

\frac{6}{( 1 - x ) ^{3}}

\frac{18}{( 1 - x ) ^{4}}

Solution steps

\frac{d}{d x} (\frac{6}{( 1 - x ) ^{3}})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 6 \frac{d}{d x} (\frac{1}{( 1 - x ) ^{3}})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= 6 \frac{d}{d x} ((1 - x)^{- 3})

Apply the chain rule:

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

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

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

= 6 (- \frac{3}{( 1 - x ) ^{4}} (- 1))

Simplify

6 (- \frac{3}{( 1 - x ) ^{4}} (- 1)) : \frac{18}{( 1 - x ) ^{4}}

= \frac{18}{( 1 - x ) ^{4}}

What is the derivative of 6/((1-x)^3) ?
The derivative of 6/((1-x)^3) is (18)/((1-x)^4)
What is the first derivative of 6/((1-x)^3) ?
The first derivative of 6/((1-x)^3) is (18)/((1-x)^4)