Limits & derivatives Flashcards
1
Q
lim(x–>a) (x^n - a^n)/(x-a) =
A
na^(n-1)
2
Q
sinx/x=
A
1
3
Q
(1-cosx)/x
A
0
4
Q
derivative of f at a
A
lim(h–>0) f’(a)=f(a+h)-f(a)/h
5
Q
derivative of f at any point
A
f’(x) lim(h–>0) f(x+h)-f(x)/h
6
Q
(u±v)’ =
A
u’ ± v’
7
Q
(uv)’=
A
uv’ + u’v
8
Q
(u/v)’=
A
(u’v - uv’)/v^2
9
Q
d(x^n)/dx
A
nx^(n-1)
10
Q
dsinx/dx
A
cosx
11
Q
dcosx/dx
A
-sinx
12
Q
dtanx/dx
A
sec^2 x
13
Q
dcosecx/dx
A
cotxcosecx
14
Q
dcotx/dx
A
-cosec^2 x
15
Q
dsecx/dx
A
secxtanx
