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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

baseb 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)/ba

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

