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Derivatives
Basic Rules and examples
15
Mathematics
12th Grade
03/21/2013
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Term

Power Rule:

f(x) = axn

 Definition
f ’(x) = anxn-1
Term
Product Rule:
f(x)g(x) 
 Definition
f ’(x)g(x) + f(x)g’(x) 
Term

Quotient Rule:

 f(x) 

g(x)

 
 Definition

 f ’(x)g(x) – f(x)g’(x)

[g(x)]2
Term

Chain Rule:

f(g(x))

 Definition
f ’(g(x))g’(x) 
Term
y = ex
 Definition
y’ = ex
Term
y = ax
 Definition
y’ = ax ln a 
Term
y = ln x 
 Definition
y’ = 1/x 
Term
y = logax 
 Definition
y’ = 1 / (x ln a ) 
Term
y = sin(x)  
 Definition
y’ = cos(x) 
Term
y = cos(x)  
 Definition
y’ = -sin(x) 
Term
y = tan(x)
 Definition
y’ = sec2(x)
Term
y = csc(x) 
 Definition
y’ = -csc(x)cot(x) 
Term
y = sec(x) 
 Definition
y’ = sec(x)tan(x) 
Term
y = cot(x) 
 Definition

y’ = -csc(x)

 
Term
y=5x3
 Definition
y'=15x2
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