What is the derivative of (x^{-2}+x)^{-3} ?

The derivative of (x^{-2}+x)^{-3} is -(3x^5(x^3-2))/((1+x^3)^4)

What is the first derivative of (x^{-2}+x)^{-3} ?

The first derivative of (x^{-2}+x)^{-3} is -(3x^5(x^3-2))/((1+x^3)^4)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

(x^{- 2} + x)^{- 3}

- \frac{3 x ^{5} ( x ^{3} - 2 )}{( 1 + x ^{3} ) ^{4}}

Solution steps

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

Apply the chain rule:

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

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

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

= - \frac{3}{( x ^{- 2} + x ) ^{4}} (- \frac{2}{x ^{3}} + 1)

Simplify

- \frac{3}{( x ^{- 2} + x ) ^{4}} (- \frac{2}{x ^{3}} + 1) : - \frac{3 x ^{5} ( x ^{3} - 2 )}{( 1 + x ^{3} ) ^{4}}

= - \frac{3 x ^{5} ( x ^{3} - 2 )}{( 1 + x ^{3} ) ^{4}}

f (x) = (x + 2 sin (x))

\int \frac{x - 3}{3 - 4 x ^{2}} d x

(4 X - 1)^{2} (3 X - 1)^{- 2}

\frac{d y}{d x} = 8 x y

\int \frac{x}{196 x ^{2} - 1} d x

What is the derivative of (x^{-2}+x)^{-3} ?
The derivative of (x^{-2}+x)^{-3} is -(3x^5(x^3-2))/((1+x^3)^4)
What is the first derivative of (x^{-2}+x)^{-3} ?
The first derivative of (x^{-2}+x)^{-3} is -(3x^5(x^3-2))/((1+x^3)^4)