What is the derivative of (3+x^5)^{2/3} ?

The derivative of (3+x^5)^{2/3} is (10x^4)/(3(3+x^5)^{1/3)}

What is the first derivative of (3+x^5)^{2/3} ?

The first derivative of (3+x^5)^{2/3} is (10x^4)/(3(3+x^5)^{1/3)}

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derivative of

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

\frac{10 x ^{4}}{3 ( 3 + x ^{5} ) ^{\frac{1}{3}}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{2}{3 ( 3 + x ^{5} ) ^{\frac{1}{3}}} \cdot 5 x^{4} : \frac{10 x ^{4}}{3 ( 3 + x ^{5} ) ^{\frac{1}{3}}}

= \frac{10 x ^{4}}{3 ( 3 + x ^{5} ) ^{\frac{1}{3}}}

\frac{d}{d x} (π \cdot x)

\frac{d}{d t} (cos (t^{2}))

\frac{d}{d x} (\frac{π}{x})

\frac{d}{d x} (- 3 x^{4} - \frac{1}{x} + x x)

x \to - \frac{π}{4} lim (- sec (2 x))

What is the derivative of (3+x^5)^{2/3} ?
The derivative of (3+x^5)^{2/3} is (10x^4)/(3(3+x^5)^{1/3)}
What is the first derivative of (3+x^5)^{2/3} ?
The first derivative of (3+x^5)^{2/3} is (10x^4)/(3(3+x^5)^{1/3)}