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

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

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

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

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derivative of

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

Solution steps

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

\frac{d}{d x} (x^{2}) = 2 x

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

Simplify

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

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

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x \to 2 lim (f (x) + 5 g (x))

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