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Derivative Rules
Derivative Rules for AP Calculus
21
Mathematics
12th Grade
10/06/2014
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Term
axn
 Definition
anxn-1
Term
f(x) • g(x)
 Definition
f(x)g'(x) + g(x)f'(x)
Term

f(x)

----------

g(x)

 Definition

g(x)f'(x) - f(x)g'(x)

-------------------------

[g(x)]2
Term
f(g(x))
 Definition
f'(g(x)) • g'(x)
Term
sinx
 Definition
cosx
Term
cosx
 Definition
-sinx
Term
tanx
 Definition
sec2x
Term
secx
 Definition
tanxsecx
Term
cscx
 Definition
-cotxcscx
Term
cotx
 Definition
-csc2x
Term
lnx
 Definition

1

----

x
Term
ex
 Definition
ex
Term
ax
 Definition
axlna
Term
logbx
 Definition

1

------

xlnb
Term
f-1(x)
 Definition

1

----------

f'(f-1(x))
Term
sin-1x
 Definition

1

----------

√(1-x2)
Term
cos-1x
 Definition

-1

----------

√(1-x2)
Term
tan-1x
 Definition

1

---------

1+x2
Term
sec-1x
 Definition

1

---------

lxl √(x2-1)
Term
csc-1x
 Definition

-1

---------

lxl√(x2-1)
Term
cot-1x
 Definition

-1

----------

x2+1
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