What is the derivative of \sqrt[3]{(x^2-1^2}) ?

The derivative of \sqrt[3]{(x^2-1^2}) is (4x)/(3(x^2-1)^{1/3)}

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

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

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

Solution steps

Apply the chain rule:

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

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

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

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

Simplify

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

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

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