What is the derivative of y=4\sqrt[3]{x^5} ?

The derivative of y=4\sqrt[3]{x^5} is (20x^4)/(3(x^5)^{2/3)}

What is the first derivative of y=4\sqrt[3]{x^5} ?

The first derivative of y=4\sqrt[3]{x^5} is (20x^4)/(3(x^5)^{2/3)}

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derivative

\frac{20 x ^{4}}{3 ( x ^{5} ) ^{\frac{2}{3}}}

Solution steps

\frac{d}{d x} (4 3 x^{5})

Take the constant out:

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

= 4 \frac{d}{d x} (3 x^{5})

Apply the chain rule:

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

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

\frac{d}{d x} (x^{5}) = 5 x^{4}

= 4 \cdot \frac{1}{3 ( x ^{5} ) ^{\frac{2}{3}}} \cdot 5 x^{4}

Simplify

4 \cdot \frac{1}{3 ( x ^{5} ) ^{\frac{2}{3}}} \cdot 5 x^{4} : \frac{20 x ^{4}}{3 ( x ^{5} ) ^{\frac{2}{3}}}

= \frac{20 x ^{4}}{3 ( x ^{5} ) ^{\frac{2}{3}}}

What is the derivative of y=4\sqrt[3]{x^5} ?
The derivative of y=4\sqrt[3]{x^5} is (20x^4)/(3(x^5)^{2/3)}
What is the first derivative of y=4\sqrt[3]{x^5} ?
The first derivative of y=4\sqrt[3]{x^5} is (20x^4)/(3(x^5)^{2/3)}