Math Derivative rules Sum and difference rule

# 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.

$f(x)=g(x)+h(x)$
$f'(x)=g'(x)+h'(x)$

### Example

$f(x)=3x^2+4x^5$

1. #### Split function into subfunctions

$g(x)=3x^2$ and $h(x)=4x^5$
2. #### Derive subfunctions

$g'(x)=6x$ and $h'(x)=20x^4$
3. $f'(x)=6x+20x^4$

A tip: Often, you can calculate the result quickly in the head and omit step 1/2.

## Difference rule

!

### Remember

A difference function is derived by deriving the subfunctions individually.

$f(x)=g(x)-h(x)$
$f'(x)=g'(x)-h'(x)$

### Example

$f(x)=7x^3-4x$

1. #### Split function into subfunctions

$g(x)=7x^3$ and $h(x)=4x$
2. #### Derive subfunctions

$g'(x)=21x^2$ and $h'(x)=4$

3. $f'(x)=21x^2-4$

A tip: Often, you can calculate the result quickly in the head and omit step 1/2.