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

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

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

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

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derivative of

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

Solution steps

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}

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

Simplify

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

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

\int x^{7} - 3 x + 2 d x

\int \frac{1}{x ln ( x ^{4} )} d x

f (x) = cos (sin (x))

f (x) = \frac{x ^{3}}{( x - 2 ) ^{2}}

\int sec^{3} (θ) d θ

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