Please e-mail me if you have any useful suggestions about this page.
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)
( cot(x) )’ = -csc2(x)
( sec(x) )’ = sec(x) tan(x)
( csc(x) )’ = -csc(x) cot(x)
( arcsin(x) )’ = 1/sqrt(1-x2)
( arccos(x) )’ = -1/sqrt(1-x2)
( arctan(x) )’ = 1/(1+x2)
( arccot(x) )’ = -1/(1+x2)
( arcsec(x) )’ = 1/sqrt(x2-1)
( arccsc(x) )’ = -1/sqrt(x2-1)
( 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 elementary practice exercises from Thomas’ Calculus:Early Transcendental Functions, 11th ed.
Section 3.1 #27-43
Section 3.2 #1-46
Section 3.3 #1-30
Section 3.4 #1-46
Section 3.5 #1-108
Section 3.6 #1-66
Section 3.7 #1-96
Section 3.8 #49-74
Section 3.10 #1-66
Other exercises in these sections are good for providing deeper insight into the derivative.
Go to
- Dr. Rickert’s MA111 page
- the Mathematics Department Home Page
- Dr. Rickert’s classes page
- Dr. Rickert’s home page