calculus

• Chain rule:

  y = [f(x)]

  dy/dx = n[f(x)]^n-1 x f'(x)
• Product rule:

  f(x) x g(x) = f'(x)g(x) + f(x)g'(x)
• Quotient rule:

  f(x)/g(x) = f'(x)g(x) - f(x)g'(x) / [g(x)]^2
• Derivation of exponentials:

  e^x = e^x

  e^f(x) = e^f(x) x f'(x)
• Logarithmic functions:

  ln x = 1/x

  ln f(x) = f'(x)/f(x)
• Exponent laws:

  e^m x e^n = e^m+n

  (e^m)^n = e^mn

  e^m/e^n = e^m-n

  e^-m = 1/e^m

  e^0 = 1
• Logarithm laws:

  ln (ab) = lna + lnb

  ln(a/b) = lna - lnb

  n lna = lna^n

  lna^-1 = ln(1/a)

  lne=1

  lne^n=n

  e^lnb = b

  ln1=0
• Trigonometric function:

  sin(x) = cos(x)

  cos(x) = -sin(x)

  tan(x) = 1/cos^2(x)

  sin(f(x)) = cos(f(x)) x f'(x)

  cos(f(x)) = -sin(f(x)) x f'(x)

  tan(f(x)) = 1/cos^2(f(x)) x f'(x)