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
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Solution assignment 01 Product and Quotient rule

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Assignment 1

Differentiate:

$y=x\sin(x)$

Solution

We use the product rule to differentiate this function with:

$f(x)=x$

and:

$g(x)=\sin(x)$

Because:

$f'(x)=1$

and:

$g'(x)=\cos(x)$

we get:

$y'=1\cdot\sin(x)+x\cos(x)=\sin(x)+x\cos(x)$

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