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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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