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Differentiation rules

With a few rules you can differentiate every polynomial. The power rule brings the exponent down in front and subtracts one from it. Constants disappear, and a sum is differentiated term by term.

(x^n)' = n x^{n-1}

power rule

(c\cdot f)' = c\cdot f'

constant factor

(f + g)' = f' + g'

sum rule

Symbols

$n$	exponent
$c$	constant

Example

$f(x) = 3x^4 - 2x + 7$ :

$f'(x) = 12x^3 - 2$ .

The constant term (here 7) always disappears when you differentiate.

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Part of Foundations of Mathematics: Introduction to derivatives.