Transcript Math 34A - University of California, Santa Barbara

Math 34A
Derivative
Rules
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB
Derivative Shortcut Rules
Power Function
d n
( x )  n  x(n1)
dx
Exponential Function
d
( Ae kx )  kA  ekx
dx
Derivative Shortcut Rules
Power Function
d n
( x )  n  x(n1)
dx
Exponential Function
d
( Ae kx )  kA  ekx
dx
Examples of Power Functions
Examples of Exponential Functions
f(x)  5x3
J(x)  5e3x
g(x)  6 x
K(x)  2e5x
5
h(x)  3
x
L(x) 
i(x)  103 x4
M(x)  10  2x
5
e3x
Rules for exponents
These should be review, but they are all important
x A  xB  x(A B)
x 
A B
 x AB
1
A
x
A
x
n
x x
1
n
Derivatives of Combinations of functions
Product Rule
Quotient Rule
(f  g)  f  g  f  g
f
f   g  f  g
( ) 
g
g2
Chain Rule
(f(g))  f(g)  g