What is the derivative of \sqrt[3]{x}on[0.1] ?

The derivative of \sqrt[3]{x}on[0.1] is (0.03333…no)/(x^{2/3)}

What is the first derivative of \sqrt[3]{x}on[0.1] ?

The first derivative of \sqrt[3]{x}on[0.1] is (0.03333…no)/(x^{2/3)}

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\frac{d}{d x} (3 x o n [0.1])

\frac{0.03333 \dots n o}{x ^{\frac{2}{3}}}

Solution steps

\frac{d}{d x} (3 x o n (0.1))

Treat

n, o

as a constant

Take the constant out:

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

= o n \cdot 0.1 \frac{d}{d x} (3 x)

Apply radical rule:

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

= o n \cdot 0.1 \frac{d}{d x} (x^{\frac{1}{3}})

Apply the Power Rule:

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

= o n \cdot 0.1 \cdot \frac{1}{3} x^{\frac{1}{3} - 1}

Simplify

o n \cdot 0.1 \cdot \frac{1}{3} x^{\frac{1}{3} - 1} : \frac{0.03333 \dots n o}{x ^{\frac{2}{3}}}

= \frac{0.03333 \dots n o}{x ^{\frac{2}{3}}}

What is the derivative of \sqrt[3]{x}on[0.1] ?
The derivative of \sqrt[3]{x}on[0.1] is (0.03333…no)/(x^{2/3)}
What is the first derivative of \sqrt[3]{x}on[0.1] ?
The first derivative of \sqrt[3]{x}on[0.1] is (0.03333…no)/(x^{2/3)}