Differentiation Flashcards
1
Q
(c)’ constant
A
0
2
Q
(cf(x))’
A
c f’(x)
3
Q
(f(x)+g(x))’ sum rule
A
f’(x)+g’(x)
4
Q
(f(x)-g(x))’ difference rule
A
f’(x)-g’(x)
5
Q
(f(x)g(x))’ product rule
A
f(x)g’(x)+ g(x)f’(x)
6
Q
(f(x)/g(x))’ quotient rule
A
( g(x)f’(x) - f(x)g’(x) ) / ( g(x) )^2
7
Q
(x^n)’ power rule
A
nx^(n-1)
8
Q
(ln|x|)’
A
1/x
9
Q
(e^x)’
A
e^x
10
Q
(a^x)’
A
a^xln(a)
11
Q
(logaX)’
A
1/(xlna)
12
Q
(sinx)’
A
cosx
13
Q
(cosx)’
A
-sinx
14
Q
(tanx)’
A
sec^2x
15
Q
(cscx)’
A
-cscxcotx
16
Q
(secx)’
A
secxtanx
17
Q
(cotx)’
A
-csc^2x
18
Q
(sin^(-1)x)’
A
1/(sqrt(1-x^2))
19
Q
(cos^(-1)x)’
A
-1/(sqrt(1-x^2))
20
Q
(tan^(-1)x)’
A
1/(1+x^2)
21
Q
(cot^(-1)x)’
A
-1/1+x^2)
22
Q
(csc^(-1)x)’
A
-1/x(sqrt(x^2-1))
23
Q
(sec^(-1)x)’
A
1/x(sqrt(x^2-1))
