MA112 "Basic Skills" summary
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You should know the definition of the derivative
Know
The Power Rule:
( xn )' = n xn-1
( sin(x) )' = cos(x)
( cos(x) )' = -sin(x)
( tan(x) )' = sec2(x)
( arcsin(x) )' = 1/sqrt(1-x2)
( arccos(x) )' = -1/sqrt(1-x2)
( arctan(x) )' = 1/(1+x2)
( sinh(x) )' = cosh(x)
( cosh(x) )' = sinh(x)
( ex ) ' = ex
( ln(x) )' = 1/x
The Product Rule: (f*g)' = f'*g + f*g'
The Quotient Rule: ( f / g )' = (g*f' - f*g') / g2
The Chain Rule: ( f(g(x)) ) ' = f'(g(x)) * g'(x)
Implicit Differentiation
The Power Rule: antiderivative of xn --> xn+1/(n+1)
antiderivative of sin(x) --> -cos(x)
antiderivative of cos(x) --> sin(x)
antiderivative of 1/(1+x2) --> arctan(x)
antiderivative of 1/sqrt(1-x2) --> arcsin(x)
antiderivative of sinh(x) --> cosh(x)
antiderivative of cosh(x) --> sinh(x)
antiderivative of ex --> ex
antiderivative of 1/x --> ln|x|
The Fundamental Theorem of Calculus
Integration by substitution
Integration by parts
Partial fractions
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