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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