What is the derivative of 7sqrt(x)-9/(x^6) ?

The derivative of 7sqrt(x)-9/(x^6) is (7x^{13/2}+108)/(2x^{13/2)sqrt(x)}

What is the first derivative of 7sqrt(x)-9/(x^6) ?

The first derivative of 7sqrt(x)-9/(x^6) is (7x^{13/2}+108)/(2x^{13/2)sqrt(x)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

7 x - \frac{9}{x ^{6}}

\frac{7 x ^{\frac{13}{2}} + 108}{2 x ^{\frac{13}{2}} x}

Solution steps

\frac{d}{d x} (7 x - \frac{9}{x ^{6}})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (7 x) - \frac{d}{d x} (\frac{9}{x ^{6}})

\frac{d}{d x} (7 x) = \frac{7}{2 x}

\frac{d}{d x} (\frac{9}{x ^{6}}) = - \frac{54}{x ^{7}}

= \frac{7}{2 x} - (- \frac{54}{x ^{7}})

Simplify

\frac{7}{2 x} - (- \frac{54}{x ^{7}}) : \frac{7 x ^{\frac{13}{2}} + 108}{2 x ^{\frac{13}{2}} x}

= \frac{7 x ^{\frac{13}{2}} + 108}{2 x ^{\frac{13}{2}} x}

What is the derivative of 7sqrt(x)-9/(x^6) ?
The derivative of 7sqrt(x)-9/(x^6) is (7x^{13/2}+108)/(2x^{13/2)sqrt(x)}
What is the first derivative of 7sqrt(x)-9/(x^6) ?
The first derivative of 7sqrt(x)-9/(x^6) is (7x^{13/2}+108)/(2x^{13/2)sqrt(x)}