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

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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 · 2018-04-29T17:44:43

$\frac{d y}{d x} = x + x^{- 3}$ $dy/dx=x+x^-3$

Explanation:

$differentiate using the power rule$ $"differentiate using the "color(blue)"power rule"$

$∙ x \frac{d}{d x} (a x^{n}) = n a x^{n - 1}$ $•color(white)(x)d/dx(ax^n)=nax^(n-1)$

$y = \frac{1}{2} x^{2} - \frac{1}{2} x^{- 2}$ $y=1/2x^2-1/2x^-2$

$\Rightarrow \frac{d y}{d x} = (2 \times \frac{1}{2}) x^{2 - 1} - (- 2 \times \frac{1}{2}) x^{- 2 - 1}$ $rArrdy/dx=(2xx1/2)x^(2-1)-(-2xx1/2)x^(-2-1)$

$\Rightarrow \frac{d y}{d x} = x + x^{- 3}$ $color(white)(rArrdy/dx)=x+x^-3$

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

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