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

The derivative of (x^{-3}+4(x^{-2}-5x)) is (2x^3-5)/(x^6)-20

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

The first derivative of (x^{-3}+4(x^{-2}-5x)) is (2x^3-5)/(x^6)-20

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

\frac{2 x ^{3} - 5}{x ^{6}} - 20

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{- 3} + 4, g = x^{- 2} - 5 x

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

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

\frac{d}{d x} (x^{- 2} - 5 x) = - \frac{2}{x ^{3}} - 5

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

Simplify

(- \frac{3}{x ^{4}}) (x^{- 2} - 5 x) + (- \frac{2}{x ^{3}} - 5) (x^{- 3} + 4) : \frac{2 x ^{3} - 5}{x ^{6}} - 20

= \frac{2 x ^{3} - 5}{x ^{6}} - 20

\frac{\partial}{\partial x} (\frac{x ^{2} - y ^{2}}{x y})

\int 1 + y^{2} d y

\int_{- 1}^{2} 4 x^{3} - 3 x^{2} d x

\int sin (3 x) + e^{2 x} d x

\int (\frac{x sin ^{2} ( x )}{2}) d x

What is the derivative of (x^{-3}+4(x^{-2}-5x)) ?
The derivative of (x^{-3}+4(x^{-2}-5x)) is (2x^3-5)/(x^6)-20
What is the first derivative of (x^{-3}+4(x^{-2}-5x)) ?
The first derivative of (x^{-3}+4(x^{-2}-5x)) is (2x^3-5)/(x^6)-20