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

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

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

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

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\frac{5 ^{\frac{1}{3}}}{3 x ^{\frac{2}{3}}}

Solution steps

Apply the chain rule:

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

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

\frac{d}{d x} (5 x) = 5

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

Simplify

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

= \frac{5 ^{\frac{1}{3}}}{3 x ^{\frac{2}{3}}}

x \to 0 + lim (cot (3 x))

\frac{\partial}{\partial y} (3 x y^{2})

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

\frac{\partial}{\partial y} (5 y)

x \to \infty lim (x \frac{1}{x})

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