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

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

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

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

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

Solution steps

Apply the chain rule:

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

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

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

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

Simplify

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

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

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