What is the derivative of (x-1/x ^3) ?

The derivative of (x-1/x ^3) is 3x^2+3/(x^4)-3/(x^2)-3

What is the first derivative of (x-1/x ^3) ?

The first derivative of (x-1/x ^3) is 3x^2+3/(x^4)-3/(x^2)-3

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

3 x^{2} + \frac{3}{x ^{4}} - \frac{3}{x ^{2}} - 3

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= 3 x^{2} + \frac{3}{x ^{4}} - \frac{3}{x ^{2}} - 3

What is the derivative of (x-1/x ^3) ?
The derivative of (x-1/x ^3) is 3x^2+3/(x^4)-3/(x^2)-3
What is the first derivative of (x-1/x ^3) ?
The first derivative of (x-1/x ^3) is 3x^2+3/(x^4)-3/(x^2)-3