If y = xn then the ratio of relative errors in y and x is

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n : 1 	ext { Let } ∆ x/x 	ext { be the relative error in x and} ∆ y/y 	ext { be the error in y } . 	ext { Now,} y = x^n \Rightarrow dy/dx = n x^{n - 1} \Rightarrow ∆ y/y = \frac{n x^{n - 1}}{y}dx \Rightarrow ∆ y/y = \frac{n x^{n - 1}}{x^n}dx = n∆ x/x \Rightarrow ∆ y/y: ∆ x/x = n: 1

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