What is the derivative of \sqrt[3]{27x^2}-1/(\sqrt[3]{27x^2}) ?

The derivative of \sqrt[3]{27x^2}-1/(\sqrt[3]{27x^2}) is 2/(x^{1/3)}+2/(9x^{5/3)}

What is the first derivative of \sqrt[3]{27x^2}-1/(\sqrt[3]{27x^2}) ?

The first derivative of \sqrt[3]{27x^2}-1/(\sqrt[3]{27x^2}) is 2/(x^{1/3)}+2/(9x^{5/3)}

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\frac{2}{x ^{\frac{1}{3}}} + \frac{2}{9 x ^{\frac{5}{3}}}

Solution steps

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{2}{x ^{\frac{1}{3}}} - (- \frac{2}{9 x ^{\frac{5}{3}}})

Simplify

= \frac{2}{x ^{\frac{1}{3}}} + \frac{2}{9 x ^{\frac{5}{3}}}

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x \to 0 - lim (- 1)

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What is the derivative of \sqrt[3]{27x^2}-1/(\sqrt[3]{27x^2}) ?
The derivative of \sqrt[3]{27x^2}-1/(\sqrt[3]{27x^2}) is 2/(x^{1/3)}+2/(9x^{5/3)}
What is the first derivative of \sqrt[3]{27x^2}-1/(\sqrt[3]{27x^2}) ?
The first derivative of \sqrt[3]{27x^2}-1/(\sqrt[3]{27x^2}) is 2/(x^{1/3)}+2/(9x^{5/3)}