What is the derivative of \sqrt[4]{1/x} ?

The derivative of \sqrt[4]{1/x} is -1/(4x^{5/4)}

What is the first derivative of \sqrt[4]{1/x} ?

The first derivative of \sqrt[4]{1/x} is -1/(4x^{5/4)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

- \frac{1}{4 x ^{\frac{5}{4}}}

Solution steps

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{4 ( \frac{1}{x} ) ^{\frac{3}{4}}} (- \frac{1}{x ^{2}}) : - \frac{1}{4 x ^{\frac{5}{4}}}

= - \frac{1}{4 x ^{\frac{5}{4}}}

What is the derivative of \sqrt[4]{1/x} ?
The derivative of \sqrt[4]{1/x} is -1/(4x^{5/4)}
What is the first derivative of \sqrt[4]{1/x} ?
The first derivative of \sqrt[4]{1/x} is -1/(4x^{5/4)}