Respuesta:
y'= 96x^3 - 279/2 x^2 + 32x + 89/2
Explicación paso a paso:
F(x) = (3x^2 - 6x + 5 ) (1/2 x + 8x^2 - 7)
y = (3x^2 - 6x + 5 ) (1/2 x + 8x^2 - 7)
y' = (2(3x)^2-1 - 6(1) + 0) (1/2 x + 8x^2 - 7) + (3x^2 - 6x + 5 ) (1/2(1)+2(8x)^2-1)-0)
y'= (6x-6) (1/2 x + 8x^2 - 7) + (3x^2 - 6x + 5 ) (1/2+16x)
y'= (6x(1/2 x + 8x^2 - 7)) -6(1/2 x + 8x^2 - 7) + 1/2(3x^2 - 6x + 5 ) +16x (3x^2 - 6x + 5 )
y'= (3x^2+48x^3-42x) -3x-48x^2+42 + 3/2 x^2 -3x+5/2 + 48x^3 - 96x^2 +80x
agrupamos terminos semejantes y operamos:
y'= 48x^3+48x^3 + 3x^2-48x^2+3/2x^2-96x^2 + 80x-42x-3x -3x+42+5/2
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Respuesta:
y'= 96x^3 - 279/2 x^2 + 32x + 89/2
Explicación paso a paso:
F(x) = (3x^2 - 6x + 5 ) (1/2 x + 8x^2 - 7)
y = (3x^2 - 6x + 5 ) (1/2 x + 8x^2 - 7)
y' = (2(3x)^2-1 - 6(1) + 0) (1/2 x + 8x^2 - 7) + (3x^2 - 6x + 5 ) (1/2(1)+2(8x)^2-1)-0)
y'= (6x-6) (1/2 x + 8x^2 - 7) + (3x^2 - 6x + 5 ) (1/2+16x)
y'= (6x(1/2 x + 8x^2 - 7)) -6(1/2 x + 8x^2 - 7) + 1/2(3x^2 - 6x + 5 ) +16x (3x^2 - 6x + 5 )
y'= (3x^2+48x^3-42x) -3x-48x^2+42 + 3/2 x^2 -3x+5/2 + 48x^3 - 96x^2 +80x
agrupamos terminos semejantes y operamos:
y'= 48x^3+48x^3 + 3x^2-48x^2+3/2x^2-96x^2 + 80x-42x-3x -3x+42+5/2
y'= 96x^3 - 279/2 x^2 + 32x + 89/2