What is the derivative of sqrt(x)+1/(x^3) ?

The derivative of sqrt(x)+1/(x^3) is (x^{7/2}-6)/(2x^{7/2)sqrt(x)}

What is the first derivative of sqrt(x)+1/(x^3) ?

The first derivative of sqrt(x)+1/(x^3) is (x^{7/2}-6)/(2x^{7/2)sqrt(x)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

\frac{x ^{\frac{7}{2}} - 6}{2 x ^{\frac{7}{2}} x}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (x) = \frac{1}{2 x}

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

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

Simplify

\frac{1}{2 x} - \frac{3}{x ^{4}} : \frac{x ^{\frac{7}{2}} - 6}{2 x ^{\frac{7}{2}} x}

= \frac{x ^{\frac{7}{2}} - 6}{2 x ^{\frac{7}{2}} x}

What is the derivative of sqrt(x)+1/(x^3) ?
The derivative of sqrt(x)+1/(x^3) is (x^{7/2}-6)/(2x^{7/2)sqrt(x)}
What is the first derivative of sqrt(x)+1/(x^3) ?
The first derivative of sqrt(x)+1/(x^3) is (x^{7/2}-6)/(2x^{7/2)sqrt(x)}