derivative + integral rules

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10 Terms

1
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constant rule

f’( c ) = 0, c is a constant

2
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constant multiple rule

f’( c f(x) ) = c f’(x)

3
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power rule

f’( x^n ) = n x^(n-1)

4
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sum and difference rule

f’( f(x) ± g(x) ) = f’(x) + g’(x)

5
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product rule

f’( f(x)g(x) ) = f’(x) g(x) + f(x) g’(x)

6
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quotient rule

f’( f(x) / g(x) ) = ( f’(x) g(x) - f(x) g’(x) ) / ( g(x) )^2

7
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chain rule

f’( f(g(x)) ) = f’( g(x) ) g’(x)

8
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integral power rule

∫x^n dx = 1/(n+1) x^(n+1) + C , n ≠ -1

9
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integral constant multiples rule

∫kf(x) dx = k ∫ f(x)

10
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integral sums and differences rule

∫[ f(x) ± g(x) ] = ∫f(x) dx ± ∫g(x) dx