1
Q
f(x) = sin(x)
A
f’(x) = cos(x)
2
Q
f(x) = cos(x)
A
f’(x) = -sin(x)
3
Q
f(x) = tan(x)
A
f’(x) = sec^2(x)
4
Q
f(x) = sec(x)
A
f’(x) = sec(x)tan(x)
5
Q
f(x) = csc(x)
A
f’(x) = -csc(x)cot(x)
6
Q
f(x) = cot(x)
A
f’(x) = -csc^2(x)
7
Q
f(x) = e^x
A
f’(x) = e^x
8
Q
f(x) = ln(x)
A
f’(x) = 1/x
9
Q
f(x) = a^x
A
f’(x) = (a^x)lna
10
Q
f(x) = log(a)x
A
f’(x) = 1/(xlna)
11
Q
f(x) = arcsinx = sin^-1x
A
f’(x) = 1/sqrt(1-x^2)
12
Q
f(x) = arccosx = cos^-1x
A
f’(x) = -1/sqrt(1-x^2)
13
Q
f(x) = arctanx = tan^-1x
A
f’(x) = 1/(1+x^2)
14
Q
g(x) = f^-1(x)
A
g’(x) = 1/f’(g(x))
15
Q
Limit Definition
A
f’(x) = lim(h->0) [f(x+h)-f(x)]/h
16
Q
Power Rule
A
[x^n]’ = nx^(n-1)
17
Q
Product Rule
A
[fg]’ = fg’ + f’g
18
Q
Quotient Rule
A
[f/g]’ = (gf’-fg’)/g^2
19
Q
Chain Rule
A
[f(g(x))]’ = f’(g(x))g’(x)
AP Calculus AB
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