Derivadas

Roxy Hughes
Mind Map by Roxy Hughes, updated more than 1 year ago
Roxy Hughes
Created by Roxy Hughes over 5 years ago
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The different formulas for deriving functions.
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Derivadas
1 Reglas de derivación elementales
1.1 d/dx c = 0
1.1.1 La derivada de una constante es 0
1.2 d/dx cx = c
1.2.1 La derivada de una constante c, por x es la constante. Por lo tanto: la derivada de una recta y = mx + b, es igual a su pendiente, m.
1.3 d/dx cx^n = ncx^n-1
1.4 d/dx mr)x^n = d/dx x^n/m = n/m x^(n/m)-1
1.5 d/dx [g(x)]^n = n[g(x)]^n-1 * d/dx g(x)
1.5.1 Función de funciones
1.6 d/dx [g(x) +- h(x)] = g'(x) +- h'(x)
1.6.1 La derivada de la suma o resta de dos (o más) funciones es la suma de sus derivadas.
1.7 d/dx [g(x)h(x)] = g(x)h'(x) + h(x)g'(x)
1.7.1 Producto de dos funciones
1.8 d/dx g(x)/h(x) = [h(x)g'(X) - g(x)h'(x)] / [h(x)]^2
1.8.1 Cociente de dos funciones
2 d/dx = f'(x) = y'
2.1 f' (x)
2.1.1 1ra derivada
2.2 f" (x)
2.2.1 2da derivada
3 Reglas de derivación de funciones transcendentes
3.1 d/dx lnu = 1/u d/dx u
3.2 d/dx logv = loge/v d/dx v
3.3 d/dx a^u = a^u lna d/dx u
3.4 d/dx e^v = e^v d/dx v
3.5 d/dx senu = cosu d/dx u
3.6 d/dx cosv = -senv d/dx v
3.7 d/dx tanu =sec^2 u d/dx u
3.8 d/dx cotv = -csc^2 v d/dx v
3.9 d/dx secu = secu tanu d/dx u
3.10 d/dx cscv = -cscv ctgv d/dx v
3.11 d/dx arcsenu = 1/[sqr(1-u^2)] d/dx u
3.12 d/dx arccosv = -1/[sqr(1-v^2)] d/dx v
3.13 d/dx arctanu = 1/[1 + u^2] d/dx u
3.14 arccotv = -1/[1 + v^2] d/dx v
3.15 d/dx arcsecu = 1/[u sqr(u^2 -1)] d/dx u
3.16 d/dx arccscv = -1/[v sqr(v^2 -1)] d/dx v
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