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Popular Calculus >

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

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Graph

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d er i v a t i v e \frac{1}{( 1 - t ^{2} ) ^{\frac{1}{2}}}

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Frequently Asked Questions (FAQ)

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