Question

Calcula la derivada de las siguientes funciones:
a) f (x) = 2x + 5
b) f (x) = 22 + 3x− 1
c) f(x) = x3 − 2x2 + x + 12
d) f (x) = 3x4 + 125

Answer 1

Respuesta:

A)f(x) = 2x+5

f ' (x) = d/dx[2x+5]

f ' (x) = d/dx[2x]+d/dx[5]

f ' (x) = d/dx[2x]+0

f ' (x) = 2×d/dx[x]

f ' (x) = 2(1)

f ' (x) = 2

B)f(x) = 22+3x-1

f ' (x) = d/dx[22+3x-1]

f ' (x) = d/dx[22]+d/dx[3x]-d/dx[1]

f ' (x) = 0+3×d/dx[x]-0

f ' (x) = 3×1

f ' (x) = 3

C)f(x) = x^3+2x^2+x+12

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

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

f ' (x) = 3x^2+2×d/dx[x^2]+1+0

f ' (x) = 3x^2+2(2x)+1

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

D)f(x) = 3x^4+125

f ' (x) = d/dx[3x^4+125]

f ' (x) = d/dx[3x^4]+d/dx[125]

f ' (x) = 3×d/d[x^4]+d/dx[125]

f ' (x) = 3(4x^3)+0

f ' (x) = 12x^3

Explicación paso a paso: