derivatives Flashcards
1
Q
d/dx [cu]
A
cu’
2
Q
d/dx [u ± v]
A
u’ ± v’
3
Q
d/dx [uv]
A
uv’ + u’v
4
Q
d/dx [u/v]
A
(vu’ - uv’) / v²
5
Q
d/dx [c]
A
0
6
Q
d/dx [uⁿ]
A
nuⁿ⁻¹ u’
7
Q
d/dx [x]
A
1
8
Q
d/dx [|u|]
A
(u / |u| ) (u’), u≠0
9
Q
d/dx [ln u]
A
u’ / u
10
Q
d/dx [eᵘ]
A
eᵘu’
11
Q
d/dx [logₐ u]
A
u’ / ((ln a) u)
12
Q
d/dx [aᵘ]
A
(ln a)aᵘu’
13
Q
d/dx [sin u]
A
(cos u)u’
14
Q
d/dx [cos u]
A
-(sin u)u’
15
Q
d/dx [tan u]
A
(sec² u)u’
16
Q
d/dx [cot u]
A
-(csc² u)u’
17
Q
d/dx [sec u]
A
(sec u tan u)u’
18
Q
d/dx [csc u]
A
-(csc u cot u)u’
19
Q
d/dx [arcsin u]
A
(u’ / √1-u²)
20
Q
d/dx [arccos u]
A
(-u’ / √1-u²)
21
Q
d/dx [arctan u]
A
(u’ / 1+u²)
22
Q
d/dx [arccot u]
A
(-u’ / 1+u²)
23
Q
d/dx [arcsec u]
A
(u’ / |u| √u²-1)
24
Q
d/dx [arccsc u]
A
(-u’ / |u| √u²-1)
