What is the derivative of ((x+2/x)^3+((x-2)/x)^3) ?

The derivative of ((x+2/x)^3+((x-2)/x)^3) is -(48)/(x^3)

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

The first derivative of ((x+2/x)^3+((x-2)/x)^3) is -(48)/(x^3)

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

- \frac{48}{x ^{3}}

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d x} ((\frac{x + 2}{x})^{3}) = - \frac{6 ( x + 2 ) ^{2}}{x ^{4}}

\frac{d}{d x} ((\frac{x - 2}{x})^{3}) = \frac{6 ( x - 2 ) ^{2}}{x ^{4}}

= - \frac{6 ( x + 2 ) ^{2}}{x ^{4}} + \frac{6 ( x - 2 ) ^{2}}{x ^{4}}

Simplify

- \frac{6 ( x + 2 ) ^{2}}{x ^{4}} + \frac{6 ( x - 2 ) ^{2}}{x ^{4}} : - \frac{48}{x ^{3}}

= - \frac{48}{x ^{3}}

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\frac{d y}{d x} = x^{2} + 12 x y

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What is the derivative of ((x+2/x)^3+((x-2)/x)^3) ?
The derivative of ((x+2/x)^3+((x-2)/x)^3) is -(48)/(x^3)
What is the first derivative of ((x+2/x)^3+((x-2)/x)^3) ?
The first derivative of ((x+2/x)^3+((x-2)/x)^3) is -(48)/(x^3)