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Popular >

derivative of \sqrt[4]{1+x^3}

Solution

Solution

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

Solution steps

Apply the chain rule:

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

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

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

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

Simplify

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

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

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Frequently Asked Questions (FAQ)

What is the derivative of \sqrt[4]{1+x^3} ?
The derivative of \sqrt[4]{1+x^3} is (3x^2)/(4(1+x^3)^{3/4)}
What is the first derivative of \sqrt[4]{1+x^3} ?
The first derivative of \sqrt[4]{1+x^3} is (3x^2)/(4(1+x^3)^{3/4)}