What is (\partial)/(\partial x)(\sqrt[3]{(x+1)^2}) ?

The answer to (\partial)/(\partial x)(\sqrt[3]{(x+1)^2}) is 2/(3(x+1)^{1/3)}

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(\partial)/(\partial x)(\sqrt[3]{(x+1)^2})

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

Solution steps

Apply the chain rule:

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

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

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

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

Simplify

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

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

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What is (\partial)/(\partial x)(\sqrt[3]{(x+1)^2}) ?
The answer to (\partial)/(\partial x)(\sqrt[3]{(x+1)^2}) is 2/(3(x+1)^{1/3)}