Try the “Did I forget how to differentiate?” Questions at top
Did I?
The moment of truth
xx 22 23 3xx 34 4xx
18965 523 xxxx 17854 9091215 xxxx
11 vbvb vxbxxx
qxpxqxpx 23 223 11 rtrt crxatxcxax
xxx 2626 45
26830 34 xx
C2 Differentiation
• Know how differentiate for any power as a rational number
• Understand the use of Indices for C2 Diff.• Be able to make use of indices’ rules to
differentiate those fractions & surds
Rule for Differentiation
1 nn anxaxa = constant, n = power
1) Times the constant by the power
2) Minus one from the power
Rule for Differentiation
1 nn anxax2x ,1 a 2n
1 2 )( 12x x2
Rule for Differentiation
1 nn anxax54x ,4 a 5n
4 5 )( 15x 420x
Rule for Differentiation
1 nn anxaxThis equation is a tool for any differentiation question!
Treat this like a machine/tool
Find out what a and n are, and substitute them
Rule for Differentiation
1 nn anxax1x ,1 a 1n
1 1 )( 11x 2 x
Rule for Differentiation
1 nn anxax
x
1,1 a 1n
2 x
1x
2
1
x
Rule for Differentiation
1 nn anxax32 x ,2 a 3n
2 3 )( 13x 46 x
Rule for Differentiation
1 nn anxax21x ,1 a 2
1n
1 21 )( 12
1 x 2
1
21 x
Rule for Differentiation
1 nn anxax
x ,1 a 21n
21
21 x
x2
1
Indices StuffYou need to know the following:
nnx
x
1nn xx1
nmm
n xx n
m
mn
xx
1
Example
3xy
?dx
dy 43 x
Example
34xy
?dx
dy31
3
4x
Example
43
2 xy
?dx
dy47
4
6 x
Example
xxy
?dx
dy
23xy
21
2
3x
Try out the questions at the bottom
Solutions on the back. Q7 on back for the crazy.
Try out the 3 exam questions on Back
Independent StudyExercise 8A p125 (solution p422) & Exercise 8B p129 (solution p422)