derivatives Flashcards
1
Q
product rule:
g(x) * h(x)
A
g’(x) * h(x) + g(x) * h’(x)
2
Q
quotient rule:
g(x) / h(x)
A
g’(x) * h(x) - g(x) * h’(x) / (h(x))^2
3
Q
chain rule:
g(h(x))
A
g’(h(x)) * h’(x)
4
Q
e^u
A
e^u * u’
5
Q
a^x
A
a^x * ln(a) (where a>0 and a!= 1)
6
Q
ln(u)
A
u’ / u
7
Q
loga(x)
A
1 / x * ln(a)
8
Q
sin(u)
A
cos(u) * u’
9
Q
cos(x)
A
-sin(x)
10
Q
tan(x)
A
sec^2(x)
11
Q
reciprocal rule:
1/f(x)
A
(- f’(x)) / f(x)^2
12
Q
c^ax
A
ac^x
13
Q
Definition of a derivative (formula)
A
L= lim h->0 for (f(x + h) - f(x)) / h
