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Popular >

derivative of ((x-1)/x)^3

Solution

derivative of

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

Solution

\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}}

Graph

Popular Examples

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derivative of tan((x^2)/3)derivative of

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d/(d{x)}(cos^3({x})cos^4({y})cos^5({z}))

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derivative of (x^3)/(4-x)derivative of

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derivative of 1/(4x^2)derivative of

\frac{1}{4 x ^{2}}

Frequently Asked Questions (FAQ)

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)