What is the derivative of 5\sqrt[3]{x^2} ?

The derivative of 5\sqrt[3]{x^2} is (10)/(3x^{1/3)}

What is the first derivative of 5\sqrt[3]{x^2} ?

The first derivative of 5\sqrt[3]{x^2} is (10)/(3x^{1/3)}

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\frac{d}{d x} (5 3 x^{2})

\frac{10}{3 x ^{\frac{1}{3}}}

Solution steps

\frac{d}{d x} (5 3 x^{2})

Take the constant out:

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

= 5 \frac{d}{d x} (3 x^{2})

Apply the chain rule:

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

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

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

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

Simplify

5 \cdot \frac{1}{3 ( x ^{2} ) ^{\frac{2}{3}}} \cdot 2 x : \frac{10}{3 x ^{\frac{1}{3}}}

= \frac{10}{3 x ^{\frac{1}{3}}}

x \to - 6 lim (6 x + 1)

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

(- 8.1) (2.7)

\frac{( e ^{x} )}{5 - x}

(1 + x e^{\frac{2}{x}})^{^{'}}

What is the derivative of 5\sqrt[3]{x^2} ?
The derivative of 5\sqrt[3]{x^2} is (10)/(3x^{1/3)}
What is the first derivative of 5\sqrt[3]{x^2} ?
The first derivative of 5\sqrt[3]{x^2} is (10)/(3x^{1/3)}