Differentiation Flashcards
1
Q
What is differentiation from first principles?
(Expression)
A
F’(x) = lim f (x+h) - f (x)
———————
h
2
Q
What do different values of derivatives tell us?
A
F’(x) < 0: decreasing
F’(x) = 0: stationary point
F’(x) > 0: increasing
3
Q
What do different values of second derivatives tell us?
A
F”(x) < 0: concave/max
F”(x) = 0: point of inflection
F”(x) > 0: convex/min
4
Q
Derivative of ax^n
A
anx^(n-1)
5
Q
Derivative of a^x
A
ln a • a^x
6
Q
Derivative of e^x
A
e^x
7
Q
Derivative of ln x
A
1/x
8
Q
Derivative of Sin kx
A
K Cos kx
9
Q
Derivative of Cos kx
A
-k Sin kx
10
Q
Derivative of Tan x
A
Sec^2 x
11
Q
Derivative of Sec x
A
Sec x Tan x
12
Q
Derivative of Cot x
A
- Cosec^2 x
13
Q
Derivative of Cosec x
A
Cosec x Cot x
14
Q
What is the chain rule?
A
f (x) ~> f ‘(x) • x’
15
Q
What is quotient rule?
A
u/v ~> vu’-uv’
———
v^2
