{"id":680,"date":"2016-09-06T15:56:37","date_gmt":"2016-09-06T15:56:37","guid":{"rendered":"http:\/\/wordpress.rose-hulman.edu\/rickert\/?page_id=680"},"modified":"2016-09-16T18:41:23","modified_gmt":"2016-09-16T18:41:23","slug":"ma112-basic-skills-summary","status":"publish","type":"page","link":"https:\/\/wordpress.rose-hulman.edu\/rickert\/ma112-basic-skills-summary\/","title":{"rendered":"MA112 “Basic Skills” Summary"},"content":{"rendered":"

Please e-mail me<\/u><\/a> if you have any useful suggestions about this page.<\/p>\n

\n

You should know the definition of the derivative<\/p>\n

Know<\/p>\n

The Power Rule<\/strong>: ( xn<\/sup><\/em> )’ = n xn-1<\/sup><\/em><\/p>\n

( sin(x<\/em>) )’ = cos(x<\/em>)<\/p>\n

( cos(x<\/em>) )’ = -sin(x<\/em>)<\/p>\n

( tan(x<\/em>) )’ = sec2<\/sup>(x<\/em>)<\/p>\n

 <\/p>\n

( arcsin(x<\/em>) )’ = 1\/sqrt(1-x<\/em>2<\/sup>)<\/p>\n

( arccos(x<\/em>) )’ = -1\/sqrt(1-x<\/em>2<\/sup>)<\/p>\n

( arctan(x<\/em>) )’ = 1\/(1+x<\/em>2<\/sup>)<\/p>\n

 <\/p>\n

( sinh(x<\/em>) )’ = cosh(x<\/em>)<\/p>\n

( cosh(x<\/em>) )’ = sinh(x<\/em>)<\/p>\n

 <\/p>\n

( ex<\/sup><\/em> ) ‘ = ex<\/sup><\/em><\/p>\n

( ln(x<\/em>) )’ = 1\/x<\/em><\/p>\n

 <\/p>\n

The Product Rule<\/strong>: (f*g)’ = f’*g + f*g’<\/p>\n

The Quotient Rule<\/strong>: ( f \/ g )’ = (g*f’ – f*g’) \/ g2<\/sup><\/p>\n

The Chain Rule<\/strong>: ( f(g(x)) ) ‘ = f'(g(x)) * g'(x)<\/p>\n

Implicit Differentiation<\/strong><\/p>\n

\n

The Power Rule<\/strong>: antiderivative of xn<\/sup><\/em> –> xn+1<\/sup><\/em>\/(n<\/em>+1)<\/p>\n

antiderivative of sin(x<\/em>) –> -cos(x<\/em>)<\/p>\n

antiderivative of cos(x<\/em>) –> sin(x<\/em>)<\/p>\n

antiderivative of 1\/(1+x<\/em>2<\/sup>) –> arctan(x<\/em>)<\/p>\n

antiderivative of 1\/sqrt(1-x<\/em>2<\/sup>) –> arcsin(x<\/em>)<\/p>\n

antiderivative of sinh(x<\/em>) –> cosh(x<\/em>)<\/p>\n

antiderivative of cosh(x<\/em>) –> sinh(x<\/em>)<\/p>\n

antiderivative of ex<\/sup><\/em> –> ex<\/sup><\/em><\/p>\n

antiderivative of 1\/x<\/em> –> ln|x<\/em>|<\/p>\n

The Fundamental Theorem of Calculus<\/strong><\/p>\n

Integration by substitution<\/strong><\/p>\n

Integration by parts<\/strong><\/p>\n

Partial fractions<\/strong><\/p>\n

\n

Go to<\/p>\n