def. of derivatives Flashcards
1
Q
f’(x)=lim as x approaches 0
A
f(x+h)-f(x)/h
2
Q
f’(c)=lim as x approaches c
A
f(x)-f(c)/x-c
3
Q
d/dx[xⁿ]
A
n･xⁿ⁻¹
4
Q
d/dx[c f(x)]
A
cf’(x)
5
Q
d/dx[fg]
A
f’g+fg’
6
Q
d/dx[f/g]
A
f’g-fg’/g²
7
Q
d/dx[sin x]
A
cos x
8
Q
d/dx[cos x]
A
-sin x
9
Q
d/dx[tan x]
A
sec² x
10
Q
d/dx[cot x]
A
-csc² x
11
Q
d/dx[sec x]
A
sec x tan x
12
Q
d/dx[csc x]
A
-csc x cot x
13
Q
d/dx[eˣ]
A
eˣ
14
Q
d/dx[aˣ]
A
aˣ-lna
15
Q
d/dx[ln x]
A
1/x
