MA111 "Basic Skills" summary
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Each student must earn a perfect score on at least one Basic Skills Derivative quiz in MA111.
Skills quizzes will begin after midterm and will be administered by the professor in class. Additional quiz opportunities will be available through the learning center.
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
Some good practice exercises from Calculus:Early Transcendental Functions, 2nd ed., by Larsen, Hostetler & Edwards:
Section 2.2 #3-20, 37-50
Section 2.3 #15-46
Section 2.4 #9-42, 45-90, 105-120
Section 2.5 #1-20, 53-62
Section 2.6 #11-28
Section 4.9 #15-28, 53-60
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