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Popular >

derivative of \sqrt[4]{x^4-2}

Solution

\frac{d}{d x} (4 x^{4} - 2)

Solution

\frac{x ^{3}}{( x ^{4} - 2 ) ^{\frac{3}{4}}}

Solution steps

\frac{d}{d x} (4 x^{4} - 2)

Apply the chain rule:

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

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

\frac{d}{d x} (x^{4} - 2) = 4 x^{3}

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

Simplify

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

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

Graph

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x \to 0 lim (\frac{x ^{3} + 5 x}{x})

Frequently Asked Questions (FAQ)

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