Differentiation Flashcards
1
Q
Meaning of f’(x)<0
A
decreasing function
2
Q
Meaning of f’(x)=0
A
stationary function
3
Q
A
4
Q
Meaning of f’(x)>0
A
increasing function
5
Q
Meaning of f’‘(x)<0
A
Concave
Maximum
6
Q
Meaning of f’‘(x)=0
A
point of inflection
7
Q
Meaning of f’‘(x)>0
A
Convex
Minimum
8
Q
A
9
Q
Differentiate axn
A
an xn-1
9
Q
Differentiate ax
A
lna ax
10
Q
Differentiate ex
A
ex
11
Q
Differentiate e3x
A
3e3x
12
Q
Differentiate lnx
A
1/x
13
Q
Differentiate sinx
A
cosx
14
Q
Differentiate cosx
A
-sinx
15
Q
Differentiate tanx (FB)
A
sec2x
16
Q
Differentiate secx (FB)
A
secx tanx
16
Q
Differentiate cotx (FB)
A
-cosec2x
17
Q
Differentiate cosecx (FB)
A
-cosecxcotx
18
Q
Product rule: f(x)g(x)
A
f’(x)g(x) + f(x)g’(x)
19
Q
Implicit Diff: f(y) =
A
f’(y) * dy/dx
20
Q
Chain rule: f(…..) =
A
f’(…..) * (…..)’
21
Q
Reciprocal =
A
1/gradient or dx/dy
22
Q
Parametric Differentiation
A
(dy/dx) = (dy/dt) x (dt/dx)
23
Connected rates of change differentiation
(dV/dt) = (dV/...) x (.../dt)
causes other variable to cancel
24
Rate is ....
(...)/dt
