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

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

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

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

derivative of

5 3 x

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

Solution steps

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

Take the constant out:

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

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

Apply radical rule:

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

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

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= 5 \cdot \frac{1}{3} x^{\frac{1}{3} - 1}

Simplify

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

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

\frac{\partial}{\partial y} (x ln (yz))

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

\int \frac{x}{2 x - 1} d x

y^{^{'}} = \frac{x}{10 y}

\int sec (x) tan^{5} (x) d x

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