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Popular >

derivative of \sqrt[3]{5+6x^6}

Solution

derivative of

Solution

\frac{12 x ^{5}}{( 5 + 6 x ^{6} ) ^{\frac{2}{3}}}

Solution steps

Apply the chain rule:

\frac{1}{3 ( 5 + 6 x ^{6} ) ^{\frac{2}{3}}} \frac{d}{d x} (5 + 6 x^{6})

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

\frac{d}{d x} (5 + 6 x^{6}) = 36 x^{5}

= \frac{1}{3 ( 5 + 6 x ^{6} ) ^{\frac{2}{3}}} \cdot 36 x^{5}

Simplify

\frac{1}{3 ( 5 + 6 x ^{6} ) ^{\frac{2}{3}}} \cdot 36 x^{5} : \frac{12 x ^{5}}{( 5 + 6 x ^{6} ) ^{\frac{2}{3}}}

= \frac{12 x ^{5}}{( 5 + 6 x ^{6} ) ^{\frac{2}{3}}}

Popular Examples

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Frequently Asked Questions (FAQ)

What is the derivative of \sqrt[3]{5+6x^6} ?
The derivative of \sqrt[3]{5+6x^6} is (12x^5)/((5+6x^6)^{2/3)}
What is the first derivative of \sqrt[3]{5+6x^6} ?
The first derivative of \sqrt[3]{5+6x^6} is (12x^5)/((5+6x^6)^{2/3)}