Derivative rules Flashcards
1
Q
f’(x) of f(x) = u^n
A
nu^(n-1)
2
Q
f’(x) of f(x) = g(x) + h(x)
A
g’(x) + h’(x)
3
Q
f’(x) of f(x) = uv
A
u’v + v’u
4
Q
f’(x) of f(x) = u/v
A
(u’v - v’u)/v^2
5
Q
f’(x) of f(x) = sin(x)
A
cos(x)
6
Q
f’(x) of f(x) = cos(x)
A
-sin(x)
7
Q
f’(x) of f(x) = tan(x)
A
sec^2(x)
8
Q
f’(x) of f(x) = cot(x)
A
-csc^2(x)
9
Q
f’(x) of f(x) = sec(x)
A
sec(x) ⋅ tan(x)
10
Q
f’(x) of f(x) = csc(x)
A
-csc(x) ⋅ cot(x)
11
Q
f’(x) of f(x) = e^u
A
e^u ⋅ u’
12
Q
f’(x) of f(x) = ln(x)
A
1/x
13
Q
f’(x) of f(x) = u + v
A
u’ + v’
14
Q
f’(x) of f(x) = (u)^n
A
n(u)^n-1 ⋅ u’
15
Q
What is the linearization equation?
A
L(x) = f(a) + f’(a)(x-a)
16
Q
f’(x) of f(x) = cosh(x)
A
sinh(x)
17
Q
f’(x) of f(x) = sinh(x)
A
cosh(x)
18
Q
f’(x) of f(x) = tanh(x)
A
sech^2(x)
19
Q
f’(x) of f(x) = sech(x)
A
-sech(x)tanh(x)
20
Q
f’(x) of f(x) = csch(x)
A
-csch(x)coth(x)
21
Q
f’(x) of f(x) = coth(x)
A
-csch^2(x)
