Math 34A - University of California, Santa Barbara
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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(n1)
dx
Exponential Function
d
( Ae kx ) kA ekx
dx
Derivative Shortcut Rules
Power Function
d n
( x ) n x(n1)
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 AB
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