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

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{1 + x ^{3}}{1 - x ^{3}}) = \frac{6 x ^{2}}{( 1 - x ^{3} ) ^{2}}

= \frac{1}{3 ( \frac{1 + x ^{3}}{1 - x ^{3}} ) ^{\frac{2}{3}}} \cdot \frac{6 x ^{2}}{( 1 - x ^{3} ) ^{2}}

Simplify

\frac{1}{3 ( \frac{1 + x ^{3}}{1 - x ^{3}} ) ^{\frac{2}{3}}} \cdot \frac{6 x ^{2}}{( 1 - x ^{3} ) ^{2}} : \frac{2 x ^{2}}{( x ^{3} + 1 ) ^{\frac{2}{3}} ( - x ^{3} + 1 ) ^{\frac{4}{3}}}

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

x \to 8 + lim (ln (x^{2} - 64))

\frac{\partial}{\partial x} (x + \frac{1}{2} y)

\frac{1}{1 - x}, 1.1

\frac{d y}{d x}, y = 1.1 x + 0.077 x^{2}

\frac{3}{( s + 2 ) \cdot ( 4 s ^{2} + 4 s + 5 )}

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