Derivative Rules Flashcards
1
Q
(c)’ = ?
A
0
2
Q
(f + g)’ = ?
A
f’ + g’
3
Q
(fg)’ = ?
A
f’g + fg’
4
Q
(f/g)’ = ?
A
f’g - fg’ / g^2
5
Q
(sin x)’ = ?
A
cos x
6
Q
(cos x)’ = ?
A
-sin x
7
Q
(tan x)’ = ?
A
sec^2 x
8
Q
(cot x)’ = ?
A
-csc^2 x
9
Q
(sec x)’ = ?
A
sec x tan x
10
Q
(csc x)’ = ?
A
-csc x cot x
11
Q
(sin^-1 x)’ = ?
A
1 / sqrt(1 - x^2)
12
Q
(cos^-1 x)’ = ?
A
-1 / sqrt(1 - x^2)
13
Q
(tan^-1 x)’ = ?
A
1 / 1 + x^2
14
Q
(cot^-1 x)’ = ?
A
-1 / 1 + x^2
15
Q
(sec^-1 x)’ = ?
A
1 / x sqrt(x^2 - 1)
16
Q
(csc^-1 x )’ = ?
A
-1 / x sqrt(x^2 - 1)
17
Q
[f(g(x))]’ = ?
A
f’(g(x))(g(x))’
18
Q
[(g(x))^n]’ = ?
A
n(g(x))^n-1(g(x))’
19
Q
(e^x)’ = ?
A
e^x
20
Q
(ln x)’ = ?
A
1 / x
21
Q
(a^x)’ = ?
A
(a^x)(ln a)
22
Q
(log base a of x)’ = ?
A
1 / (x)(ln a)
23
Q
(e^u)’ = ?
A
(e^u)(u)’
24
Q
(ln u)’ = ?
A
u’ / u
25
(a^u)' = ?
(a^u)(u)'(ln a)
26
(log base a of u)' = ?
u' / (u)(ln a)
