7820810
Description
Flashcards by Gabino Franco, updated more than 1 year ago
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Created by Gabino Franco
almost 8 years ago
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| Question | Answer |
| Regla de la potencia f(x)= ax^n f(x)'=anx^n-1 | Ejemplo: y'=3x^3 - 2x^2- 5x + 2 y'=(3)(3)x^3-1 - (2)(2)x^2-1 - (5)(1)x^1-1 y'=9x^2-4x-5 |
| Regla del producto f(x)=(u)(v) f(x)'= (u) dv/dx + (v) du/dx | Ejemplo: y=(3x^2)(5x^3-3x) y'= 3x^2 (15x^2-3)+ (5x^3-3x)(6x) y'= 45x^4 - 9x^2 + 30x^4 - 18x^2 y'= 75x^4 - 27x^2 |
| Regla del cociente: y=u/v y'= [(v) du/dx - (u) dv/dx] / v^2 | Ejemplo: y= 3x^2 - 2x / 5x+1 y'={(5x+1)*(6x-2) - (3x^2 - 2x)(5)}/ (5x-1)^2 y'=30x^2-10x+6x-2-15x^2 + 10x / 25x^2-10x+1 y'=15x^2 - 6x - 2/ 25x^2-10x + 1 |
| Regla ln y= ln x y'= 1/ x | Ejemplo: y= ln (ln (x^2+1)) y'=1/ ln(x^2+1) 1* (1/x^2+1) * (2x/1) y'= 2x/ ln (x^2+1) (x^2+1) |
| Regla de la cadena: y= g(u) u= f(x) y=(g)(f(x)) y= gof(x) | Ejemplo: y= (x^3- 8x^-2) ^7 y= 7(x^3- 8x^-2)^6 y=(x^3- 8x^-2)^6* (7)(3x^2+ 16x^-3) y= (x^3- 8x^-2)^6 (22x^2+ 112x^-3) |
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