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Popular >

derivative of (1+1/x)^3

Solution

derivative of

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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Frequently Asked Questions (FAQ)

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