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Popular >

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

Solution

derivative of

(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

Popular Examples

slope of y=6sqrt(x)+x^2 slope

y = 6 x + x^{2}

integral of 1/(t^2sqrt(6-t^2))

\int \frac{1}{t ^{2} 6 - t ^{2}} d t

derivative of f(x)=cos(a^5+x^5)derivative of

f (x) = cos (a^{5} + x^{5})

laplacetransform f(t)=e^{,\at}laplace transform

f (t) = e^{, at}

inverse oflaplace 1/(s^2+3s+1)inverse laplace

\frac{1}{s ^{2} + 3 s + 1}

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)})