Mathemetics and Statistics explained - examples - solutions

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Solution assignment 01 Product and Quotient rule
Solution assignment 02 Product and Quotient rule
Solution assignment 03 Product and Quotient rule
Solution assignment 04 Product and Quotient rule
Solution assignment 05 Product and Quotient rule
Solution assignment 06 Product and Quotient rule
Solution assignment 07 Product and Quotient rule
Solution assignment 08 Product and Quotient rule
Solution assignment 09 Product and Quotient rule
Solution assignment 10 Product and Quotient rule
Solution assignment 11 Product and Quotient rule
Solution assignment 12 Product and Quotient rule
Solution assignment 13 Product and Quotient rule
Solution assignment 14 Product and Quotient rule
Solution assignment 15 Product and Quotient rule
Solution assignment 16 Product and Quotient rule
Solution assignment 17 Product and Quotient rule
Solution assignment 18 Product and Quotient rule
Solution assignment 19 Product and Quotient rule
Solution assignment 20 Product and Quotient rule
Solution assignment 21 Product and Quotient rule
Solution assignment 22 Product and Quotient rule
Solution assignment 23 Product and Quotient rule
Solution assignment 24 Product and Quotient rule
Solution assignment 25 Product and Quotient rule
Solution assignment 26 Product and Quotient rule
Solution assignment 27 Product and Quotient rule
Solution assignment 28 Product and Quotient rule
Solution assignment 29 Product and Quotient rule
Solution assignment 30 Product and Quotient rule

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Solution assignment 18 Product and Quotient rule

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Assignment 18

Differentiate:

$y=\displaystyle\frac{3}{x^2+1}$

Solution

Here the quotient rule has to be applied with:

$f'(x)=0$

$g'(x)=2x$

and thus:

$y'=\displaystyle\frac{(x^2+1)\cdot0-3(2x)}{(x^2+1)^2}=-\displaystyle\frac{6x}{(x^2+1)^2}$

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