boongsta said:
have u guys got any ideas to remember this easily ... or maybe someone can explain the reasoning behind the solution? its kinda hard to memorise this
You need to remember these rules:
Product rule: uv' + vu'
Example: differentiate (3x + 4)(5x + 5)
u = 3x + 4
u' = 3
v = 5x + 5
v' = 5
uv' + vu' = (3x + 4).5 + (5x + 5).3
= 15x + 20 + 15x + 15
= 30x + 35
Quotient rule: (vu' - uv')/v2
Example: differentiate (2x + 5)/3x
u = 2x + 5
u' = 2
v = 3x
v' = 3
(vu' - uv')/v
2 = [3x.2 - (2x + 5).3]/9x
2
= (6x - 6x - 15)/9x
2
= -15/9x
2
Chain rule: Not sure how I can put this, so just look at the example.
Example: differentiate (4x + 16)
15
Look at (4x + 16) as one thing, and differentiate. You get:
15(4x + 16)
14. However, you need differentiate the "insides" (that is, 4x + 16) and multiply it by the 15(4x + 16)
14.
So we end up with: 4.15(4x + 16)
14
= 60(4x + 16)
14
If anyone has a better explanation of the chain rule, post it up.