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

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

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

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

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derivative of

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

Solution steps

Take the constant out:

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

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}

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

Simplify

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

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

\int_{0}^{1} (1) d x

x e^{x} y^{^{'}} + 2 e^{x} y = 0

\int 9 - 16 x^{2} d x

\int (\frac{1}{x ^{2} - 9}) d x

x, - x + 6, 0

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