What is the derivative of \sqrt[5]{2x^3+8x} ?

The derivative of \sqrt[5]{2x^3+8x} is (6x^2+8)/(5(2x^3+8x)^{4/5)}

What is the first derivative of \sqrt[5]{2x^3+8x} ?

The first derivative of \sqrt[5]{2x^3+8x} is (6x^2+8)/(5(2x^3+8x)^{4/5)}

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derivative of

\frac{6 x ^{2} + 8}{5 ( 2 x ^{3} + 8 x ) ^{\frac{4}{5}}}

Solution steps

Apply the chain rule:

\frac{1}{5 ( 2 x ^{3} + 8 x ) ^{\frac{4}{5}}} \frac{d}{d x} (2 x^{3} + 8 x)

= \frac{1}{5 ( 2 x ^{3} + 8 x ) ^{\frac{4}{5}}} \frac{d}{d x} (2 x^{3} + 8 x)

\frac{d}{d x} (2 x^{3} + 8 x) = 6 x^{2} + 8

= \frac{1}{5 ( 2 x ^{3} + 8 x ) ^{\frac{4}{5}}} (6 x^{2} + 8)

Simplify

\frac{1}{5 ( 2 x ^{3} + 8 x ) ^{\frac{4}{5}}} (6 x^{2} + 8) : \frac{6 x ^{2} + 8}{5 ( 2 x ^{3} + 8 x ) ^{\frac{4}{5}}}

= \frac{6 x ^{2} + 8}{5 ( 2 x ^{3} + 8 x ) ^{\frac{4}{5}}}

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What is the derivative of \sqrt[5]{2x^3+8x} ?
The derivative of \sqrt[5]{2x^3+8x} is (6x^2+8)/(5(2x^3+8x)^{4/5)}
What is the first derivative of \sqrt[5]{2x^3+8x} ?
The first derivative of \sqrt[5]{2x^3+8x} is (6x^2+8)/(5(2x^3+8x)^{4/5)}