What is the derivative of (8sqrt(x)+1/(x^{-5)}) ?

The derivative of (8sqrt(x)+1/(x^{-5)}) is x^4(44sqrt(x)+5)

What is the first derivative of (8sqrt(x)+1/(x^{-5)}) ?

The first derivative of (8sqrt(x)+1/(x^{-5)}) is x^4(44sqrt(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{8 x + 1}{x ^{- 5}})

x^{4} (44 x + 5)

Solution steps

\frac{d}{d x} (\frac{8 x + 1}{x ^{- 5}})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( 8 x + 1 ) x ^{- 5} - \frac{d}{d x} ( x ^{- 5} ) ( 8 x + 1 )}{( x ^{- 5} ) ^{2}}

\frac{d}{d x} (8 x + 1) = \frac{4}{x}

\frac{d}{d x} (x^{- 5}) = - \frac{5}{x ^{6}}

= \frac{\frac{4}{x} x ^{- 5} - ( - \frac{5}{x ^{6}} ) ( 8 x + 1 )}{( x ^{- 5} ) ^{2}}

Simplify

\frac{\frac{4}{x} x ^{- 5} - ( - \frac{5}{x ^{6}} ) ( 8 x + 1 )}{( x ^{- 5} ) ^{2}} : x^{4} (44 x + 5)

= x^{4} (44 x + 5)

\int x^{n + 2} d x

\int \frac{4 x ^{2} + 9 x + 4}{( x ^{2} + 1 ) ^{2}} d x

\int \frac{( 1 + x ) ^{2}}{x} d x

\int + \frac{1}{x ^{2} + a ^{2}} d x

\frac{d y}{d x} = 4 y e^{x + 4}

What is the derivative of (8sqrt(x)+1/(x^{-5)}) ?
The derivative of (8sqrt(x)+1/(x^{-5)}) is x^4(44sqrt(x)+5)
What is the first derivative of (8sqrt(x)+1/(x^{-5)}) ?
The first derivative of (8sqrt(x)+1/(x^{-5)}) is x^4(44sqrt(x)+5)