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

The derivative of \sqrt[3]{(4x^3+2x^5}) is (5(12x^2+2)(4x^3+2x)^{2/3})/3

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

The first derivative of \sqrt[3]{(4x^3+2x^5}) is (5(12x^2+2)(4x^3+2x)^{2/3})/3

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\frac{5 ( 12 x ^{2} + 2 ) ( 4 x ^{3} + 2 x ) ^{\frac{2}{3}}}{3}

Solution steps

Apply the chain rule:

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

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

\frac{d}{d x} ((4 x^{3} + 2 x)^{5}) = 5 (4 x^{3} + 2 x)^{4} (12 x^{2} + 2)

= \frac{1}{3 ( ( 4 x ^{3} + 2 x ) ^{5} ) ^{\frac{2}{3}}} \cdot 5 (4 x^{3} + 2 x)^{4} (12 x^{2} + 2)

Simplify

\frac{1}{3 ( ( 4 x ^{3} + 2 x ) ^{5} ) ^{\frac{2}{3}}} \cdot 5 (4 x^{3} + 2 x)^{4} (12 x^{2} + 2) : \frac{5 ( 12 x ^{2} + 2 ) ( 4 x ^{3} + 2 x ) ^{\frac{2}{3}}}{3}

= \frac{5 ( 12 x ^{2} + 2 ) ( 4 x ^{3} + 2 x ) ^{\frac{2}{3}}}{3}

6 t - \frac{2}{t}

\frac{d}{d x} (\frac{1}{3} x^{3} - \frac{1}{2} x^{2} - 6 x)

\frac{3 s + 17}{s ^{2} + s + 1}

\int (x^{2} - 7)^{4} (2 x) d x

t^{2} y^{^{''}} + 19 t y^{^{'}} + 106 y = 0

What is the derivative of \sqrt[3]{(4x^3+2x^5}) ?
The derivative of \sqrt[3]{(4x^3+2x^5}) is (5(12x^2+2)(4x^3+2x)^{2/3})/3
What is the first derivative of \sqrt[3]{(4x^3+2x^5}) ?
The first derivative of \sqrt[3]{(4x^3+2x^5}) is (5(12x^2+2)(4x^3+2x)^{2/3})/3