What is the derivative of g(w)=9\sqrt[3]{w} ?

The derivative of g(w)=9\sqrt[3]{w} is 3/(w^{2/3)}

What is the first derivative of g(w)=9\sqrt[3]{w} ?

The first derivative of g(w)=9\sqrt[3]{w} is 3/(w^{2/3)}

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derivative of

\frac{3}{w ^{\frac{2}{3}}}

Solution steps

Take the constant out:

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

Apply radical rule:

= 9 \frac{d}{d w} (w^{\frac{1}{3}})

Apply the Power Rule:

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

= 9 \cdot \frac{1}{3} w^{\frac{1}{3} - 1}

Simplify

9 \cdot \frac{1}{3} w^{\frac{1}{3} - 1} : \frac{3}{w ^{\frac{2}{3}}}

= \frac{3}{w ^{\frac{2}{3}}}

What is the derivative of g(w)=9\sqrt[3]{w} ?
The derivative of g(w)=9\sqrt[3]{w} is 3/(w^{2/3)}
What is the first derivative of g(w)=9\sqrt[3]{w} ?
The first derivative of g(w)=9\sqrt[3]{w} is 3/(w^{2/3)}