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

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

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

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

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derivative of

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

Solution steps

Apply the chain rule:

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

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

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

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

Simplify

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

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

e^{- 8 x}

n = 0 \sum \infty e^{n}

(4 x)^{^{'}}

23 sin (x) + 2 cos (x)

\int 2 cos (10 x) d x

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