Algebra
third derivative (x^3 - 4 x^2 + 6 x - 24) - 0 d^3/dx^3((x^3 - 4 x^2 + 6 x - 24) - 0) = 6
chain rule (a mathematical problem)
The chain rule states that if a function g(x) is differentiable at the point x and a function f(x) is differentiable at the point g(x), then the composition f◦g is differentiable at x. Furthermore, let y = f(g(x)) and u = g(x), then dy/dx = dy/du·du/dx. status | proved
(dy)/(dx) = (dy)/(du)·(du)/(dx)
mathematical rules | solved mathematics problems | mathematics theorems
chain rule (a mathematical problem) | Baudet's conjecture (a mathematical problem)
The chain rule states that if a function g(x) is differentiable at the point x and a function f(x) is differentiable at the point g(x), then the composition f◦g is differentiable at x. Furthermore, let y = f(g(x)) and u = g(x), then dy/dx = dy/du·du/dx.
Baudet's conjecture posits that if C_1, C_2, ..., C_r are sets of positive integers and union _(i = 1)^rC_i = Z^+, then some C_i contains arbitrarily long arithmetic progressions.
History
| chain rule | Baudet's conjecture
formulation date | | 1926 (97 yr ago)
formulators | | PJH Baudet
status | proved | proved
proof date | | 1928 (2 years later) (95 years ago)
provers | | Bartel Leendert van der Waerden
(dy)/(dx) = (dy)/(du)·(du)/(dx)
Probability
Game of chances
32 coin tosses
all heads | 2.328×10^-10 ≈ 1 in 4294967296
all tails | 2.328×10^-10 ≈ 1 in 4294967296
16 heads and 16 tails | 0.1399 ≈ 1 in 7
at least one head | 1-2.328×10^-10 ≈ 4294967295 in 4294967296
at least one tail | 1-2.328×10^-10 ≈ 4294967295 in 4294967296
(assuming a fair coin)
Expected heads 16
probability of heads
binomial(32, x)/4294967296 for 0<=x<=32
T | T | T | T | T | T | H | T | H | T | H | T | T | T | T | H | H | T | T | T | H | T | T | T | H | T | T | T | T | H | T | H
(assuming a fair coin)
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