Maths Core 3

Functions
1. y = f(x)
  1. Composite function fg(x) can be worked out by f(g(x))
2. Transformations of graphs
e and ln
1. y=e^x is the same as x = ln(y)
  1. ln rules
    1. ln(A) + ln(B) = ln(A+B)
    2. ln(A) - ln(B) = ln(A/B)
    3. nln(A) = ln(A^n)
2. f(x) = e^x
3. f(x) = ln(x)
Triganometary
1. Minor trig functions
  1. cosec(x) = 1/sin(x)
  2. sec(x) = 1/cos(x)
  3. cot(x) = 1/tan(x)
    1. tan(x) = sin(x)/cos(x)
    2. cot(x) = cos(x)/sin(x)
2. Identities
  1. Compound angle formulae
    1. sin(A±B) = sin(A)cos(B) ± cos(A)sin(B)
    2. cos(A±B) = cos(A)cos(B) ∓ sin(A)sin(B)
    3. tan(A±B) = [tan(A) ± tan(B)] / [1 ∓ tan(A)tan(B)]
  2. Double angle formulae
    1. sin(2A) = 2sin(A)cos(A)
    2. cos(2A) = cos^2(A) - sin^2(A)
      1. cos(2A) = 2cos^2(A) - 1
      2. cos(2A) = 1- 2sin^2(A)
    3. tan(2A) = [2tan(A)] / [1 - tan^2(A)]
  3. Pythagorean identities
    1. sin^2(x) + cos^2(x) = 1
      1. sin^2(x) = 1 - cos^2(x)
      2. cos^2(x) = 1 - sin^2(x)
Differentiation
1. Chain rule
  1. y = f(g(x)) => dy/dx = f'(g(x)) . g'(x)
  2. dy/dy = dy/du . du/dx
2. Differentials
  1. y => dy/dx
  2. f(x) => f'(x)
  3. x^n => nx^(n-1)
  4. e^x => e^x
  5. ln(x) => 1/x
  6. sin(x) => cos(x)
  7. cos(x) => -sin(x)
  8. tan(x) => sec^2(x)
  9. cosec(x) => -cosec(x)cot(x)
  10. sec(x) => sec(x)tan(x)
  11. cot(x) => -cosec^2(x)
Modulus Function
1. y = |x|
  1. graph
    1. to draw graph just reflect at the point where it crosses the x axis

Zusammenfassung der Ressource

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