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Popular >

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

Solution

derivative of

f (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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x y^{2} y^{^{'}} = y^{3} - 3 x^{3}, y (1) = 6

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Frequently Asked Questions (FAQ)

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