Differentiation

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  • Created by: eleanor
  • Created on: 22-04-15 17:13
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  • Differentiation
    • Implicit Differentiation
      • this is needed when you have to differentiate an expression that contains both x and y
      • x terms: differentiate as usual  y terms: differentiate with respect to y and then write dy/dx after each term
      • differentiate each term
        • rearrange to the form dy/dx=
          • then bring all the dy/dx terms to 1 side and factorise then divide
    • Exponential Functions
      • learn the result: y=a* = dy/dx=a*ln(a)
        • remember you can use this in the chain and product as well
      • to prove it take logs of both sides then use implicit differentiation
    • Differential Equations
      • connected rates of changes
        • this is where you link 3 different variables together using chain rule
        • we want to find how the volume changes with time so dV/dt
        • v is not  function of t it is a function of r so we use chain rule
        • 1. define appropriate letters for the variables
          • 2. write down the rate of change you were given in the question as a derivative
            • 3. write down the derivative you wan to find and link it to the given one using chain rule
              • 4. differentiate and apply chain rule
      • Proportion Equations
        • these describe growth and decay
        • growth: 1. write down the proportion equation
          • dx/dt   x
          • 2, introduce a constant k so dx/dt = kx
            • 3. solve the equation through integration
              • so x = Ae
        • Decay: write down the porportion equation dm/dt  -m
          • introduce k so dm/dt= -km
            • solve to find x

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