Solution assignment 12 Product and Quotient rule

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Assignment 12

Differentiate:

y=\displaystyle\frac{1}{x-1}

Solution

We need to apply the quotient rule. In this case we have :

f(x)=1

and:

g(x)=x-1

Because we have:

f'(x)=0

and:

g'(x)=1

we can apply the quotient rule:

y'=\displaystyle\frac{(x-1)\cdot0-1\cdot1}{(x-1)^2}=-\displaystyle\frac{1}{(x-1)^2}

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