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Solution assignment 21 Product and Quotient rule

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Assignment 21

Differentiate:

y=\displaystyle\frac{x^n+1}{x^n-1}, n\neq0

Solution

It is clear that the quotient rule has to be applied.

We have:

f'(x)=g'(x)=nx^{n-1}

and thus the quotient rule yields:

y'=\displaystyle\frac{(x^n-1)nx^{n-1}-(x^n+1)nx^{n-1}}{(x^n-1)^2}=-\displaystyle\frac{2nx^{n-1}}{(x^n-1)^2}

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