What is the derivative of \sqrt[4]{(x^2+1/(x^2-1)}) ?

The derivative of \sqrt[4]{(x^2+1/(x^2-1)}) is -x/((x^2+1)^{3/4)(x^2-1)^{5/4}}

What is the first derivative of \sqrt[4]{(x^2+1/(x^2-1)}) ?

The first derivative of \sqrt[4]{(x^2+1/(x^2-1)}) is -x/((x^2+1)^{3/4)(x^2-1)^{5/4}}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

Solution steps

Apply the chain rule:

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

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

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

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

Simplify

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

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

What is the derivative of \sqrt[4]{(x^2+1/(x^2-1)}) ?
The derivative of \sqrt[4]{(x^2+1/(x^2-1)}) is -x/((x^2+1)^{3/4)(x^2-1)^{5/4}}
What is the first derivative of \sqrt[4]{(x^2+1/(x^2-1)}) ?
The first derivative of \sqrt[4]{(x^2+1/(x^2-1)}) is -x/((x^2+1)^{3/4)(x^2-1)^{5/4}}