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

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

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

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

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

Solution steps

Take the constant out:

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

Apply exponent rule:

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

= a \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

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

Simplify

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

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

\int_{0}^{100} 37 cos (\frac{x}{80}) d x

\int sin^{3} (4 x co) s^{2} 4 x d x

2 x y^{^{'}} + y = 8 x^{3}

(x, y) \to (0, 1) lim (x^{3} y)

x \to 0 lim (5 x + 2)

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