What is the derivative of (1-6ln(x)/(x^7)) ?

The derivative of (1-6ln(x)/(x^7)) is -(-42ln(x)+13)/(x^8)

What is the first derivative of (1-6ln(x)/(x^7)) ?

The first derivative of (1-6ln(x)/(x^7)) is -(-42ln(x)+13)/(x^8)

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{1 - 6 ln ( x )}{x ^{7}})

- \frac{- 42 ln ( x ) + 13}{x ^{8}}

Solution steps

\frac{d}{d x} (\frac{1 - 6 ln ( x )}{x ^{7}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 1 - 6 ln ( x ) ) x ^{7} - \frac{d}{d x} ( x ^{7} ) ( 1 - 6 ln ( x ) )}{( x ^{7} ) ^{2}}

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

\frac{d}{d x} (x^{7}) = 7 x^{6}

= \frac{( - \frac{6}{x} ) x ^{7} - 7 x ^{6} ( 1 - 6 ln ( x ) )}{( x ^{7} ) ^{2}}

Simplify

\frac{( - \frac{6}{x} ) x ^{7} - 7 x ^{6} ( 1 - 6 ln ( x ) )}{( x ^{7} ) ^{2}} : - \frac{- 42 ln ( x ) + 13}{x ^{8}}

= - \frac{- 42 ln ( x ) + 13}{x ^{8}}

\frac{d}{d x} ((sin (x))^{\frac{1}{x}})

x^{- 6}

n = 1 \sum \infty (- 1)^{n + 1} (\frac{1}{n} + \frac{1}{3 ^{n}})

\frac{\partial}{\partial x} (\frac{1}{1 - x})

x d x - y^{2} d y = 0

What is the derivative of (1-6ln(x)/(x^7)) ?
The derivative of (1-6ln(x)/(x^7)) is -(-42ln(x)+13)/(x^8)
What is the first derivative of (1-6ln(x)/(x^7)) ?
The first derivative of (1-6ln(x)/(x^7)) is -(-42ln(x)+13)/(x^8)