Differentiation Flashcards
(30 cards)
1
Q
Dx (sin x)
A
cos x
2
Q
Dx (tan x)
A
sec² x
3
Q
Dx(sec x)
A
sec x tan x
4
Q
Dx(cos x)
A
-sin x
5
Q
Dx(cot x)
A
-csc² x
6
Q
Dx (csc)
A
-csc x cot x
7
Q
Dx (e^x)
A
e^x
8
Q
Dx (a^x)
A
a^x ln a
9
Q
Dx (sin^-1 u)
A
1/√1-u^2 Dx u
10
Q
Dx (tan-¹ u)
A
1/1+u^2 Dx u
11
Q
Dx (sec^-1 u)
A
1/u√u^2-1 Dx u
12
Q
Dx (cos-¹ u)
A
-(1/√1-u^2) Dx u
13
Q
Dx (cot^-1 u)
A
-(1/1+u^2) Dx u
14
Q
Dx (csc^-1 u)
A
-(1/u√u^2-1) Dx u
15
Q
Dx (sinh u)
A
cosh u Dx u
16
Q
Dx (tanh u)
A
sech^2 u Dx u
17
Q
Dx (sech u)
A
sech u tanh u Dx u
18
Q
Dx (cosh u)
A
sinh u Dx u
19
Q
Dx (coth u)
A
-csch^2 u Dx u
20
Q
Dx (csch u)
A
-csch u coth u Dx u
21
Q
Dx (sinh-¹ u)
A
1/√u²+1 Dx u
22
Q
Dx (tanh-¹ u)
A
1/1-u² Dx u
23
Q
Dx (sech-¹ u)
A
-1/u√1-u² Dx u
24
Q
Dx (cosh-¹ u)
A
1/√u²-1 Dx u
25
Dx (coth-¹ u)
1/1-u² Dx u
26
Dx (csch-¹ u)
1/|u|√u² + 1 Dx u
27
Dx (ln u)
1/u Dx
28
Dx (log a u)
1/u (ln a) Dx u
29
product rule, quotient rule
udv + vdu , lodhi - hidlo/lo²
30
Dx[f(u)]
chain rule
f'(u) Dx u
