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Solution assignment 19 Product and Quotient rule

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Assignment 19

Differentiate:

y=\displaystyle\frac{\ln(x)}{x}

Solution

We have to use the quotient rule with:

f'(x)=\displaystyle\frac{1}{x}

g'(x)=1

and thus:

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

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