6 ms·

this might be the right place to ask: can you differentiate a recursively defined function?

• im3w1l 8y ago
  If I understand you correctly: yes. You differentiate both sides and then get an equation for the derivative.
  • deleted 8y ago
    [deleted]
• throwawayjava 8y ago
  Yes. You can also integrate a recursively defined function(s). E.g., recall your undergraduate differential equations course.
  • mlevental 8y ago
    not sure what this means?
    • EGreg 8y ago
      It means that technique is taught in the undergrad course.
      • mlevental 8y ago
        yes i'm asking which technique - the only thing i remember that vaguely resembles this is power series solutions
• danmg 8y ago
  yes. it generally won't have a closed form however.
  • deleted 8y ago
    [deleted]
• edflsafoiewq 8y ago
  Let's try pow x 0 = 1 pow x n = x * pow x (n-1) ergo pow' x 0 = 0 pow' x n = pow x (n-1) + x * pow' x (n-1) ergo pow' x 1 = pow x 0 + x * pow' x 0 = 1 + x * 0 = 1 pow' x 2 = pow x 1 + x * pow' x 1 = x + x = 2 * x pow' x 3 = pow x 2 + x * pow' x 2 = x * x + 2 * x * x = 3 * x * x
  • deleted 8y ago
    [deleted]
• perl4ever 8y ago
  Isn't differentiation itself a recursively defined function?
  • tome 8y ago
    Yes, but good luck differentiating differentiation!