Derivatives Flashcards
1
Q
Limit definition of a derivative
A
f’(x) = lim(h->0) (f(x + h) - f(x))/h if the limit exists
2
Q
m = f’(a) is the slope of?
A
The tangent line to y = f(x) at x = a
3
Q
Equation of the tangent line
A
y = f(a) + f’(a)(x-a)
4
Q
The tangent line can be?
A
Instantaneous rate of change at a point, velocity
5
Q
a’
A
0
6
Q
[f(x) + g(x)]’
A
f’(x) + g’(x)
7
Q
[f(x)g(x)]’
A
f(x)g’(x) + f’(x)g(x)
8
Q
[f(g(x)]’
A
f’(g(x))g’(x)
9
Q
[cf(x)]’
A
cf’(x)
10
Q
[f(x) - g(x)]’
A
f’(x) - g’(x)
11
Q
[f(x)/g(x)]’
A
(f’(x)g(x) - f(x)g’(x))/(g(x))^2
12
Q
[f^-1(x)]’
A
1/(f’(f^-1(x)))
13
Q
[x^a]’
A
ax^(a-1)
14
Q
[e^x]’
A
e^x
15
Q
[e^u]’
A
u’e^u
16
Q
[a^x]’
A
a^(x)lna
17
Q
[a^u]’
A
a^(u)u’lna
18
Q
[lnx]’
A
1/x
