Differentiation

• cyrusv

  10 Feb 06, 14:51

  Hey can someone explain the meaning behind the Product Rule, Qoutient Rule and most importantly first principle and chain rule
• rainee

  10 Feb 06, 14:58

  hmm it is hard to explain w/o numbers...give me some examples and i will show you the step
  
  
• pqr

  10 Feb 06, 14:58

  Originally posted by cyrusv:

  Hey can someone explain the meaning behind the Product Rule, Qoutient Rule and most importantly first principle and chain rule

  can explain thru wording alone?
  
  best is to show and talk in person
• rainee

  10 Feb 06, 15:03

  I iwll give one basic example...for product rule
  
  2x * (x+1)^2
  
  so basically you can divide this into two parts:
  
  Part 1: 2x
  
  Part 2: (x+1)^2
  
  so first differentiate one part, and then times with part 2 without changing anything in part 2:
  
  Differentiate Part 1=2
  
  Times with Part 2: 2*(x+1)^2
  
  then differentiate part 2, then times with part 1 without changing anything in part 1:
  
  Differentiate part 2: 2(x+1)*1
  
  Times with part 1: 2x*2(x+1)
  
  Add them both
  
  2*(x+1)^2 + 4x*(x+1)
  
  
• ndmmxiaomayi

  10 Feb 06, 15:47

  Originally posted by cyrusv:

  Hey can someone explain the meaning behind the Product Rule, Qoutient Rule and most importantly first principle and chain rule

  First Principle: http://www.mathsyear2000.org/alevel/pure/purtutdiffir.htm
  
  Chain Rule: http://archives.math.utk.edu/visual.calculus/2/chain_rule.4/
  
  http://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/chainruledirectory/ChainRule.html
  
  http://www.math.hmc.edu/calculus/tutorials/chainrule/
  
  http://web.mit.edu/wwmath/calculus/differentiation/chain.html
  
  http://www.ugrad.math.ubc.ca/coursedoc/math100/notes/derivative/chain.html
• CoolMyth

  10 Feb 06, 19:55

  Originally posted by cyrusv:

  Hey can someone explain the meaning behind the Product Rule, Qoutient Rule and most importantly first principle and chain rule

  Product Rule:
  
  Let y = f[g(x)], example, f = x^2, g = x+1 --> f[g(x)] = (x+1)^2 (Composition of functions)
  
  dy/dx = f'[g(x)] * g'(x) where f' is the first derivative of f.
  
  Quotient Rule:
  
  Let y = f(x)/g(x)
  
  --> dy/dx = {[g(x) * f'(x)] - [f(x) * g'(x)]}/[g(x)]^2
  
  First Principle:
  
  Essentially, this is talking about the reasoning behind differentiation. Basically, the idea comes from trying to plot a straight line tangent to a point and taking its gradient as its derivative. The idea of limits come into place into the derivation. I now also cannot remember the definition of differentiation of first principle off-hand. Need to go and check.
  
  Chain Rule:
  
  Let y = f(x) * g(x)
  
  --> dy/dx = f(x) * g'(x) + f'(x) * g(x)
  
  Some guy called Lebiniz(sp?) showed this and this is also called the Lebiniz's Rule.
  
  The Product Rule, Quotient Rule and Chain Rule can all be derived using First Principle. I don't think I want to go into that.
• cyrusv

  17 Mar 06, 09:41

  ty