1
Q
Power rule
A
(x^n)’ = nx^(n-1)
2
Q
Constant Multiple
A
(cu)’=cu’
3
Q
Sum
A
(u+v)’ = u’ +v’
4
Q
Difference
A
(u-v)’ = u’-v’
5
Q
Product
A
(uv)’ = u’v + uv’
6
Q
Quotient
A
(u/v) = vu’-uv’/v^2
7
Q
Chain/composition
A
dy/dx= dy/du * du/dx
8
Q
Sin(u)
A
cos(u) * du/dx
9
Q
Cos(u)
A
-sin(u) * du/dx
10
Q
csc(u)
A
-csc(u)cot(u) * du/dx
11
Q
sec(u)
A
sec(u)tan(u) * du/dx
12
Q
tan(u)
A
sec^2(u) * du/dx
13
Q
cot(u)
A
-csc^2(u) * du/dx
14
Q
arcsin(u)
A
1/sqrt(1-u^2)
15
Q
arccos(u)
A
-1/sqrt(1-u^2)
16
Q
arccsc(u)
A
-1/abs(x)sqrt(u^2-1)
17
Q
arcsec(u)
A
1/abs(x)sqrt(u^2-1)
18
Q
arctan(u)
A
1/u^2+1
19
Q
arccot(u)
A
-1/u^2+1
20
Q
(f^-1(x))’
A
1/f’(f^-1(x))
21
Q
(e^u)’
A
e^u * du/dx
22
Q
(a^u)
A
(a^u)(lna) * du/dx
23
Q
ln(u)
A
1/absu * du/dx
24
Q
loga(u)
A
1/ulna * du/dx
AP Calc
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