Calculus Midterm Flashcards
1
Q
d/dx (cosu)
A
-(sinu) u’
2
Q
d/dx (cos (kx))
A
-ksin(kx)
3
Q
d/dx (tanx)
A
sec^2(x)
4
Q
d/dx (tanu)
A
(sec^2u) u’
5
Q
d/dx (cot (x)
A
-csc^2 x
6
Q
d/dx (cotu)
A
-(csc^2u)u’
7
Q
d/dx (sin(x))
A
cosx
8
Q
d/dx (sin(u))
A
(cosu)u’
9
Q
d/dx (sin(kx))
A
kcos(kx)
10
Q
d/dx (cosx)
A
-sinx
11
Q
d/dx (secx)
A
secxtanx
12
Q
d/dx (secu)
A
(secutanu) u’
13
Q
d/dx (cscx)
A
-cscxcotx
14
Q
d/dx (cscu)
A
-(cscucotu)u’
15
Q
Factor theorem
A
If P(x) is a polynomial and P(a)=0 then x-a is a factor of P(x)
16
Q
a/b - c/d
A
(ad-bc)/bd
17
Q
When direct substitution in a limit results in a nonzero number/zero
A
limit is either +infinity or -infinity or does not exist.
18
Q
sin(0)
A
0
19
Q
cos (0)
A
1
20
Q
sin (pi/2)
A
1
21
Q
Power Rule
A
d/dx x^n = nx^n-1
22
Q
Definition of a derivative
A
lim h->0 f(x+h)-f(x)/h
23
Q
Derivative of a sum
A
(f + g)’ = f’ + g’
24
Q
Chain rule
A
d/dx f(g(x)) = f’(g(x)) g’(x)
25
Exponential Derivative
d/dx (e^x) = e^x)
26
Exponential derivative chain rule
d/dx (e^u) = (e^u)u'
27
Exponential derivative special case
d/dx e^kx = ke^kx
28
Log Derivative
d/dx ln(x) = 1/x
29
log derivative chain rule form
d/dx ln(u) = u'/u
30
product rule
d/dx (fg) = f'g + fg'
31
ln (1)
0
32
ln(e)
0
