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Popular >

derivative of (x^2-1/(x^2)^6)

Solution

\frac{d}{d x} ((x^{2} - \frac{1}{x ^{2}})^{6})

Solution

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

Solution steps

\frac{d}{d x} ((x^{2} - \frac{1}{x ^{2}})^{6})

Apply the chain rule:

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

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

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

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

Graph

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\int_{\frac{5}{2}}^{5} 25 - x^{2} d x

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\int \frac{sin ( 2 x )}{46 + cos ^{2} ( x )} d x

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Frequently Asked Questions (FAQ)

What is the derivative of (x^2-1/(x^2)^6) ?
The derivative of (x^2-1/(x^2)^6) is 6(x^2-1/(x^2))^5(2x+2/(x^3))
What is the first derivative of (x^2-1/(x^2)^6) ?
The first derivative of (x^2-1/(x^2)^6) is 6(x^2-1/(x^2))^5(2x+2/(x^3))