Question

determina las derivadas de las siguientes funciones.

1.- f (x) = 3 X³ + 5 X² – 3 X + 6 f´(x) =

2.- f (x) = 4 X³ – 3 X²+ 2 X + 34 f´(x) =

3.- f (x) = 7 X⁵ + 12 X³ – 3 X² + 2X f´(x) =

4.- f (x) = 6 X³– X² + 15 X + 40 f´(x) =

5.- f (x) = 6 X⁵ – X⁴ + 15 X²– X f´(x) =​

Answer 1

Respuesta:

f(x) = 3x^3+5x^2-3x+6

f ' (x) = d/dx[ 3x^3+5x^2-3x+6 ]

f ' (x) = d/dx[3x^3]+d/dx[5x^2]-d/dx[3x]-d/dx[6]

f ' (x) = 3×d/dx[x^3]+5×d/dx[x^2]-3×d/dx[x]+0

f ' (x) = 3(3x^2)+5(2x)-3(1)+0

f ' (x) = 9x^2+10x-3+0

f ' (x) = 9x^2+10x-3

f(x) = 4x^3-3x^2+2x+34

f ' (x) = d/dx[4x^3-3x^2+2x+34 ]

f ' (x) = d/dx[4x^3]-d/dx[3x^2]+d/dx[2x]+d/dx[34]

f ' (x) = 4×d/dx[x^3]-3×d/dx[x^2]+2×d/dx[x]+0

f ' (x) = 4(3x^2)-3(2x)+2(1)+0

f ' (x) = 12x^2-6x+2.

f(x) =7x^5+12x^3-3x^2+2x

f ' (x) = d/dx [ 7x^5+12x^3-3x^2+2x ]

f ' (x) = d/dx[7x^5]+d/dx[12x^3]-d/dx[3x^2]+d/dx[2x]

f ' (x) = 7×d/dx[x^5]+12×d/dx[x^3]-3×d/dx[x^2]+2×d/dx[x]

f ' (x) = 7(5x^4)+12(3x^2)-3(2x)+2(1)

f ' (x) = 35x^4+36x^2-6x+2

f(x) = 6x^3-x^2+15x+40

f ' (x) = d/dx[6x^3-x^2+15x+40]

f ' (x) = d/dx[6x^3]-d/dx[x^2]+d/dx[15x]+d/dx[40]

f ' (x) = 6×d/dx[x^3]+2x+15×d/dx[x]+0

f ' (x) = 6(3x^2)+2x+15(1)+0

f ' (x) = 18x^2+2x+15

f(x) = 6x^5-x^4-15x^2-x

f ' (x) = d/dx[6x^5-x^4-15x^2-x]

f ' (x) = 6×d/dx[x^5]-d/dx[x^4]-15×d/dx[x^2]-d/dx[x]

f ' (x) = 6(5x^4)-4x^3-15(2x)-1

f ' (x) = 30x^4-4x^3-30x-1

Explicación paso a paso:

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