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power rule
multiply original by exponent (if constant), then reduce exponent by 1
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chain rule
take the derivative of the outside function times the derivative of the inside function
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product rule
deriv the first times second plus first times deriv second
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quotient rule
deriv first times second minus first deriv second divided by second squared
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differentiability
implies continuity
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indefinite integral
g(x)=integral f(x)dx <=> g'(x)=f'(x)
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power rule (integral)
increase exponent by 1, then divide by new exponent and add C
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natural exponential integral
eu + C
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base-b exponential
to differentiate, multiply by ln b and to integrate, divide by ln b (plus C)
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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
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fundamental theorem of calculus
f integral and g(x)= integral f(x)dx=>intrgral a to b f(x)dx=g(b)-g(a)
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fundamental theorem derivative form
g(x)=integral from a to c f(t)dt=> g'(x)=f(x)
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natural log function
the derivative is the reciprocal function
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