Unit 3 Flashcards
(37 cards)
1
Q
implicit equation
A
x and y mixed together
2
Q
implicit differentiation
A
- differentiate both sides with respect to x, adding dy/dx anytime you take the derivative of y
- collect all terms with a dy/dx on one side
- factor out dy/dx
- solve for dy/dx
3
Q
d/dx[cosx]=
A
-sinx
4
Q
d/dx[sinx]=
A
cosx
5
Q
d/dx[e^x]=
A
e^x
6
Q
d/dx[lnx]=
A
1/x
7
Q
d/dx[log(b)x]=
A
1/lnb*x
8
Q
d/dx[tanx]=
A
sec^2x
9
Q
d/dx[secx]=
A
secxtanx
10
Q
d/dx[cotx]=
A
-csc^2x
11
Q
d/dx[cscx]=
A
-cscxcotx
12
Q
cscx
A
1/sinx
13
Q
secx
A
1/cosx
14
Q
d/dx[a^x]=
A
lna*a^x
15
Q
sin^2x+cos^2x
A
1
16
Q
sin^2x=
A
(sinx)^2
17
Q
log(x^a)=
A
a(logx)
18
Q
when a variable appears in the base and exponent use
A
logarithmic differentiation
19
Q
logarithmic differentiation
A
take the log of boh sides
20
Q
e^lnx=
A
x
21
Q
inverse
A
switch x and y
22
Q
lne^x=
A
x
23
Q
g’(x)=
A
1/f’(g(x))
24
Q
h(x)=f(g(x)), h’(x)=
A
f’(g(x))*g’(x)
25
ln(ab)=
lna + lnb
26
ln(a^n)=
nlna
27
ln(a/b)
lna-lnb
28
ln(1)
0, e^0=1
29
d/dx[arcsin(u)]
u'/sqrt(1-(u)^2)
30
d/dx[arccos(u)]
-u'/sqrt(1-(u)^2)
31
d/dx[arctan(u)]
u'/1+(u)^2
32
d/dx[arccsc(u)]
-u'/|u|sqrt(u^2-1)
33
d/dx[acrsec(u)]
u'/|u|sqrt(u^2-1)
34
d/dx[acrcot(u)]
-u'/1+u^2
35
d^ny/dx^n
nth derivative
36
velocity
derivative
37
acceleration
2nd derivative
