What is the derivative of $y = \frac{1}{2} (x^{2} - x^{- 2})$ $y=1/2(x^2-x^-2)$ ?

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Answer 1 · 2018-02-05T20:25:08

$x + x^{- 3}$ $x+x^-3$

distribute the $\frac{1}{2}$ $1/2$ :
$\frac{x^{2}}{2} - \frac{x^{- 2}}{2}$ $x^2/2-x^-2/2$

use the power rule: $\frac{d}{d x} x^{n} = n x^{n - 1}$ $d/dxx^n=nx^(n-1)$
$\frac{2 x}{2} - \frac{- 2 x^{- 3}}{2}$ $(2x)/2-(-2x^-3)/2$

= $x + x^{- 3}$ $x+x^-3$

What is the derivative of y=1/2(x^2-x^-2)y=12(x2−x−2)y=1/2(x^2-x^-2)?