Sum and difference rule
The sum and difference rules state that a sum or a difference is derived in groups.
Sum rule
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Remember
A sum function is derived by deriving the subfunctions individually.
$f(x)=g(x)+h(x)$
$f'(x)=g'(x)+h'(x)$
$f(x)=g(x)+h(x)$
$f'(x)=g'(x)+h'(x)$
Example
$f(x)=3x^2+4x^5$
Split function into subfunctions
$g(x)=3x^2$ and $h(x)=4x^5$Derive subfunctions
$g'(x)=6x$ and $h'(x)=20x^4$- $f'(x)=6x+20x^4$
A tip: Often, you can calculate the result quickly in the head and omit step 1/2.
Difference rule
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Remember
A difference function is derived by deriving the subfunctions individually.
$f(x)=g(x)-h(x)$
$f'(x)=g'(x)-h'(x)$
$f(x)=g(x)-h(x)$
$f'(x)=g'(x)-h'(x)$
Example
$f(x)=7x^3-4x$
Split function into subfunctions
$g(x)=7x^3$ and $h(x)=4x$Derive subfunctions
$g'(x)=21x^2$ and $h'(x)=4$- $f'(x)=21x^2-4$
A tip: Often, you can calculate the result quickly in the head and omit step 1/2.