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Mrs Hindle’s C3 Flashy Cards!
Differentiating a quotient
(ie. one function of x divided by another)
Bottom x diff. top - Top x diff. bottom
Bottom ²
Mrs Hindle’s C3 Flashy Cards!
Differentiating a Product
(ie. one function of x multiplied by another)
Second x diff. first
+ First x diff. Second
Mrs Hindle’s C3 Flashy Cards!
Differentiation Reminder
When you’re doing a complicated
differentiation keep remembering:
“Multiply by the differential
derivative”
Mrs Hindle’s C3 Flashy Cards!
Integration Reminder
When you’re doing a complicated integration
keep remembering:
“Divide by the differential
derivative”
Mrs Hindle’s C3 Flashy Cards!
Trig Identities to learn
Tan x = sin x
cos x
;
Sec x =
1 ;
cos x
Cosec x =
1
sin x
;
Cot x =
cos²x + sin²x = 1
;
sec²x = tan²x + 1
1 ;
tan x
Mrs Hindle’s C3 Flashy Cards!
Rules of Logarithms
ln a + ln b = ln ab
ln a - ln b = ln (a/b)
a ln b = ln ba
ln 1 = 0
ln e = 1 = log 10
Mrs Hindle’s C3 Flashy Cards!
Useful Integrals
y
 y dx
sin x
-cos x
cos x
sin x
sec² x
tan x
sin ax
-
1
cos ax
a
1/x
ln x
eax
1 ax
e
a
Mrs Hindle’s C3 Flashy Cards!
Useful Differentials
y
dy
dx
sin x
cos x
tan x
sin ax
ln x
eax
cos x
-sin x
sec² x
a cos ax
1/x
aeax
Mrs Hindle’s C3 Flashy Cards!
Trig Identities
tanx =
sin x
cos x
sec x =
1
cos x
cot x =
1
tan x
sec²x = tan²x + 1
cosec²x = cot²x + 1
1
cosec x =
sin x
Mrs Hindle’s C3 Flashy Cards!
Further Trig Identities
sin 2x = 2 sin x cos x
cos 2x = cos²x - sin²x
cos 2x = 2cos²x - 1
cos 2x = 1 - 2sin²x
tan 2x = 2 tan x
1 - tan²x
Mrs Hindle’s C3 Flashy Cards!
Exact Angle Values
0º
30º
45º
60º
90º
180º
Sin
0
1
2
2
1

2
2
3
2
1
0
Cos
1
3
2
2
1

2
2
1
2
0
-1
Tan
0

0
3
3

1
3
1
3
Mrs Hindle’s C3 Flashy Cards!
Rules of Logarithms
ln a + ln b = ln ab
ln a - ln b = ln (a/b)
a ln b = ln ba
ln 1 = 0
ln e = 1 = log 10
Mrs Hindle’s C3 Flashy Cards!
More logarithm notes
ab = c
b = logac
To convert between different bases use:
logac = logbc
logbc
Mrs Hindle’s C3 Flashy Cards!
Expressions of the form asinθ + bcosθ
For positive values of a and b
asinθ + bcosθ = Rsin (θ + α)
asinθ - bcosθ = Rsin (θ - α)
acosθ + bsinθ = Rcos (θ - α)
acosθ - bsinθ = Rcos (θ + α)
for all of these R > 0, 0º< α < 90 º
Mrs Hindle’s C3 Flashy Cards!
Differentiating – function of a function
If y = [f(x)]n
dy
Then
= n [f(x)]n-1 f’(x)
dx
In simple terms pretend you are doing a basic
differentiation question but at the end multiply by the
differential derivative
Mrs Hindle’s C3 Flashy Cards!
Differentiating – chain rule
Substitute the ‘inside’ function for U
When y = [f(x)]n
Let U = f(x)
dU
= f’(x) and
dx
so y = [U]n
dy
= n(U) n-1
dx
Then use :
= dy x dU
dy
dx
dx
dx