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

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

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

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

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\frac{2}{x ^{\frac{5}{3}}}

Solution steps

Simplify

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

Apply exponent rule:

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

= - 3 \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

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

Simplify

- 3 (- \frac{1}{3 ( x ^{2} ) ^{\frac{4}{3}}} \cdot 2 x) : \frac{2}{x ^{\frac{5}{3}}}

= \frac{2}{x ^{\frac{5}{3}}}

y = 6 - x^{2}, y = 26 - 9 x

y^{^{'''}} + y = 0

x \to 9 lim (4 \cdot a + x)

x \to 5 - lim (\frac{x ^{2}}{x ^{2} + 6})

\int 9 \frac{x ^{3}}{x ^{7}} d x

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