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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d y}{d x} = \frac{x}{2 y ^{2}}, y (0) = 1

y^{^{'}} - e^{9 x + y} = 0

\int 2 cos^{4} (3 x) d x

y^{^{''}} - 4 y^{^{'}} + 13 y = sin (x) - e^{3 x} + 5

(x^{3} - 16 x)^{8}

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