Question

se realiza con la ley de cadena
$y=\left(3x-2\right)^3$

Answer 1

Respuesta:

y = (3x-2)³

y' = ((3x-2)³)'

y' = ((3x-2)³)'×(3x-2)' ;

y' = (3(3x-2)²)×(3x-2)' ; (3x-2)² = (3x)²-2(3x)(2)+(-2)² = 9x²-12x+4

y' = (3(9x²-12x+4))×(3x-2)' ; (3x-2)' = (3x)'-(2)' = (3)(x)'-(2)' = 3(1)-0 = 3

y' = 3(9x²-12x+4)(3)

y' = (3×3)(9x²-12x+4)

y' = 9(9x²-12x+4)

y' = 9(9x²)-9(12x)+9(4)

y' = 81x²-108x+36

R// Por ende , la derivada de la función " y = (3x-2)³ " es " y' = 81x²-108x+36 " .