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

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

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

The first derivative of 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}}}

\frac{d}{d x} (x + \frac{3}{x} + 5)

\frac{\partial}{\partial x} (tan (\frac{x}{2}))

y^{^{'''}} + 4 y^{^{''}} - 35 y^{^{'}} - 150 y = 0

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

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

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