What is the derivative of \sqrt[7]{u^5} ?

The derivative of \sqrt[7]{u^5} is (5u^4)/(7(u^5)^{6/7)}

What is the first derivative of \sqrt[7]{u^5} ?

The first derivative of \sqrt[7]{u^5} is (5u^4)/(7(u^5)^{6/7)}

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derivative of

\frac{5 u ^{4}}{7 ( u ^{5} ) ^{\frac{6}{7}}}

Solution steps

Apply the chain rule:

\frac{1}{7 ( u ^{5} ) ^{\frac{6}{7}}} \frac{d}{d u} (u^{5})

= \frac{1}{7 ( u ^{5} ) ^{\frac{6}{7}}} \frac{d}{d u} (u^{5})

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

= \frac{1}{7 ( u ^{5} ) ^{\frac{6}{7}}} \cdot 5 u^{4}

Simplify

\frac{1}{7 ( u ^{5} ) ^{\frac{6}{7}}} \cdot 5 u^{4} : \frac{5 u ^{4}}{7 ( u ^{5} ) ^{\frac{6}{7}}}

= \frac{5 u ^{4}}{7 ( u ^{5} ) ^{\frac{6}{7}}}

y^{^{'}} = x^{2} (1 + y^{2})

42 (7 P + 5)^{5}

y^{^{'}} = \frac{x ( y + 1 )}{y ( x + 2 )}

y^{^{'}} - y = 2 e^{2 t}

\int 15 sin^{5} (x) d x

What is the derivative of \sqrt[7]{u^5} ?
The derivative of \sqrt[7]{u^5} is (5u^4)/(7(u^5)^{6/7)}
What is the first derivative of \sqrt[7]{u^5} ?
The first derivative of \sqrt[7]{u^5} is (5u^4)/(7(u^5)^{6/7)}