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

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

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

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

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

Solution steps

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d}{d x} (x^{\frac{3}{5}} x^{3} + 5)

\frac{d}{d θ} (4 - θ^{2} sin (θ))

\frac{\partial}{\partial x} (\frac{1}{2 x + 3 y})

y = 3 - 2 x + 4 x^{3}, (- 1, 1)

\int 1 + cos (x) d x

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