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power rule
multiply original by exponent (if constant), then reduce exponent by 1
chain rule
take the derivative of the outside function times the derivative of the inside function
product rule
deriv the first times second plus first times deriv second
quotient rule
deriv first times second minus first deriv second divided by second squared
differentiability
implies continuity
indefinite integral
g(x)=integral f(x)dx <=> g'(x)=f'(x)
power rule (integral)
increase exponent by 1, then divide by new exponent and add C
natural exponential integral
e
u
+ C
base-b exponential
to differentiate, multiply by ln
b
and to integrate, divide by ln
b
(plus C)
mean value theorem
f
different (a,b)
f
cont [a,b] => at least one number c such that
f
'(c)=
f(b) - f(a)/b-a
fundamental theorem of calculus
f integral and g(x)= integral f(x)dx=>intrgral a to b f(x)dx=g(b)-g(a)
fundamental theorem derivative form
g(x)=integral from a to c f(t)dt=> g'(x)=f(x)
natural log function
the derivative is the reciprocal function
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Author
ht2lvu
ID
61350
Card Set
Cumulative Vocab
Description
AP Calculus
Updated
2011-01-23T00:22:13Z
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