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
16
Q
d/dx[logₐx]
A
1/x(lna)
17
Q
d/dx [g(a)]
A
1/f’(g(x))
17
Q
d/dx [f(g(x))]
A
f’(g(x)) ･ g’(x)
18
Q
d/dx [arcsin x]
A
1/√1-x^2
18
Q
d/dx [arctan x]
A
1/1+x^2
18
Q
d/dx [arcsec x]
A
1/|x|√x^2-1
18
Q
d/dx [arccos x]
A
-1/√1-x^2
19
Q
d/dx [arccot x]
A
-1/1+x^2
20
Q
d/dx [arccsc x]
A
-1/|x|√x^2-1
