kristoferssolo/Theory-of-Algorithms-Cheatsheet
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log in derivation tab.; derivation rules; exponentiation rules

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jorenchik 2025-06-15 09:56:36 +03:00
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@ -1065,6 +1065,7 @@ Ir spēkā sakarība $"INDSET"(G, k) = "CLIQUE"(G, k)$.
$ e^x $, $ e^x $, "",
$ a^x $, $ a^x ln(a) $, $ a > 0 $,
$ ln(x) $, $ 1 / x $, "",
$ log_a (x) $, $ 1 / (x ln(a)) $, "",
$ 1 / x $, $ -1 / x^2 $, "",
$ 1 / x^n $, $ -n / x^(n+1) $, "",
$ sqrt(x) $, $ 1 / (2 sqrt(x)) $, "",
@ -1072,6 +1073,64 @@ Ir spēkā sakarība $"INDSET"(G, k) = "CLIQUE"(G, k)$.
)
]
== Atvasinājumu īpašības
#context [
#set text(size: 11pt)
#show math.equation: set text(weight: 400, size: 11pt)
#table(
columns: 3,
[*Rule Name*], [*Function*], [*Derivative*],
[Summa], [$ f(x) + g(x) $], [$ f'(x) + g'(x) $],
[Starpība], [$ f(x) - g(x) $], [$ f'(x) - g'(x) $],
[Reizinājums], [$ f(x) * g(x) $],
[
$
f'(x) * g(x) + \
f(x) * g'(x)
$
],
/*
[Quotient Rule], [$ (f'(x) * g(x) - f(x) * g'(x)) / (g(x))^2 $], [$ (f'(x) * g(x) - f(x) * g'(x)) / (g(x))^2 $],
[Chain Rule], [$ f(g(x)) $], [$ f'(g(x)) * g'(x) $],
[Euler’s Number Exponent Rule], [$ e^x $], [$ e^x $],
[Constant Exponent Rule], [$ a^x $], [$ a^x * ln(a) $],
[Natural Log Rule], [$ ln(x) $], [$ 1 / x $],
[Logarithm Rule], [$ log_a(x) $], [$ 1 / (x * ln(a)) $],
[Sine Rule], [$ sin(x) $], [$ cos(x) $],
[Cosine Rule], [$ cos(x) $], [$ -sin(x) $],
[Tangent Rule], [$ tan(x) $], [$ sec^2(x) $],
[Cosecant Rule], [$ csc(x) $], [$ -csc(x) * cot(x) $],
[Secant Rule], [$ sec(x) $], [$ sec(x) * tan(x) $],
[Cotangent Rule], [$ cot(x) $], [$ -csc^2(x) $],
*/
)
]
== Kāpinājumu īpašības
#context [
#set text(size: 11pt)
#show math.equation: set text(weight: 400, size: 11pt)
#table(
columns: 2,
[*Rule Name*], [*Formula*],
[Reizinājums], [$ a^m * a^n = a^(m+n) $],
[Dalījums], [$ a^m / a^n = a^(m-n) $],
[Pakāpes pakāpe], [$ (a^m)^n = a^(m*n) $],
[Reizinājuma pakāpe], [$ (a*b)^m = a^m * b^m $],
[Dalījuma pakāpe], [$ (a/b)^m = a^m / b^m $],
[0-pakāpe], [$ a^0 = 1 $],
[Negatīva pakāpe], [$ a^(-m) = 1 / a^m $],
[Saikne ar sakni], [$ a^(m/n) = root(n, a^m) $],
)
]
== Noderīgas izteiksmes laika analīzē<time_analysis_expressions>
$