Differentiation Flashcards
1
Q
First principles differentiation
A
f’(x) = lim h -> 0 (f(x+h) - f(x) / h
2
Q
First Derivative meanings
A
<0 decreasing, =0 stationary, >0 increasing
3
Q
Second Derivative meanings
A
<0 concave/max, =0 inflection, >0 convex/min
4
Q
ax^n derivative
A
anx^(n-1)
5
Q
a^x derivative
A
lna . a^x
6
Q
e^x derivative
A
e^x
7
Q
lnx derivative
A
1/x
8
Q
sinx derivative
A
cosx
9
Q
cosx derivative
A
-sinx
10
Q
tanx derivative
A
sec^2 x
11
Q
secx derivative
A
secxtanx
12
Q
cotx derivative
A
-cosec^2 x
13
Q
cosecx derivative
A
-cosecxcotx
14
Q
f(blah), chain rule
A
f’(blah) x blah’
15
Q
uv, product rule
A
uv’ + u’v
16
Q
u/v, quotient rule
A
(vu’ - uv’) / v^2
17
Q
f(y), implicit
A
f’(y) x dy/dx
18
Q
Reciprocal rule for differentiation
A
dy/dx = 1/dx/dy
19
Q
Parametric rule for differentiation
A
dy/dx = dy/dt / dx/dt
20
Q
Connected rates of change rule for differentiation
A
dV/dt = dV/blah x blah/dt
