What is the derivative of (-6/((1+x)^4)) ?

The derivative of (-6/((1+x)^4)) is (24)/((1+x)^5)

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

The first derivative of (-6/((1+x)^4)) is (24)/((1+x)^5)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} (\frac{- 6}{( 1 + x ) ^{4}})

\frac{24}{( 1 + x ) ^{5}}

Solution steps

\frac{d}{d x} (\frac{- 6}{( 1 + x ) ^{4}})

Simplify

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

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

- \frac{4}{( 1 + x ) ^{5}} \frac{d}{d x} (1 + x)

= - \frac{4}{( 1 + x ) ^{5}} \frac{d}{d x} (1 + x)

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

= - 6 (- \frac{4}{( 1 + x ) ^{5}} \cdot 1)

Simplify

- 6 (- \frac{4}{( 1 + x ) ^{5}} \cdot 1) : \frac{24}{( 1 + x ) ^{5}}

= \frac{24}{( 1 + x ) ^{5}}

f (x) = (x^{2} + 1)^{x + 1}, at x = 0

\frac{d}{d x} (cos (\frac{1 - e ^{9 x}}{1 + e ^{9 x}}))

\int 2 x + 5 x^{- 2} d x

\frac{d ^{2}}{d x ^{2}} (17 e^{x^{2}})

\int (7 x^{3} - 7)^{4} x^{2} d x

What is the derivative of (-6/((1+x)^4)) ?
The derivative of (-6/((1+x)^4)) is (24)/((1+x)^5)
What is the first derivative of (-6/((1+x)^4)) ?
The first derivative of (-6/((1+x)^4)) is (24)/((1+x)^5)