5a Differentiation Flashcards
1
Q
xn
A
n xn-1
2
Q
[f(x)]n
Chain Rule
A
n [f(x)]n-1 f’(x)
3
Q
f(x)g(x)
Product Rule
A
f’(x)g(x) + f(x)g’(x)
4
Q
f(x)/ g(x)
Quotient Rule
A
[f’(x)g(x) - f(x)g’(x)]/ g2(x)
5
Q
dx/dy
A
1/ (dy/dx)
6
Q
ex
A
ex
7
Q
ef(x)
A
ef(x) f’(x)
8
Q
ln x
A
1/x
9
Q
ln[(f(x)], f(x) > 0
A
[1/f(x)] f’(x) = f’(x)/ f(x)
10
Q
sin x
A
cos x
11
Q
sin[f(x)]
A
cos[f(x)] f’(x)
12
Q
sinn[f(x)]
A
n [sin(f(x))]n-1 [cos f(x)] f’(x)
13
Q
cos x
A
-sin x
14
Q
cos[f(x)]
A
-sin[f(x)] f’(x)
15
Q
cosn[f(x)]
A
n [cos(f(x))]n-1 [-sin f(x)] f’(x)
16
Q
tan x
A
sec2x
17
Q
tan[f(x)]
A
sec2[f(x)] f’(x)
18
Q
tann[f(x)]
A
n [tan(f(x))]n-1 [sec2 f(x)] f’(x)
19
Q
cotan x
A
-cosec2(x)
20
Q
cotan[f(x)]
A
-cosec2[f(x)] f’(x)
21
Q
Implicit Differentiation
A
- Apply Chain Rule to every term especially if differentiating y!
- Look out for Product Rule!
22
Q
Parametric Equation
A
- Find Cartesian Equation by making t the subject in either equation and doing substitution.
- Find dy/dx using Rate of Change equation.
