Cómo resolver la derivada f(t)= (4x-2)^6/3x^2+7

Pienso que la función debería ser

f (x) = (4 x - 2)⁶ / (3 x² + 7)

Primera, usa la regla del cociente:

df/dx = ((3 x² + 7) • d/dx [(4 x - 2)⁶] - (4 x - 2)⁶ • d/dx [3 x² + 7]) / (3 x² + 7)²

Calcula las derivadas que quedan. Para la primera, usa las reglas de la potencia y de la cadena:

d/dx [(4 x - 2)⁶] = 6 (4 x - 2)⁵ d/dx [4 x - 2] = 24 (4 x - 2)⁵

d/dx [3 x² + 7] = 6 x

Entonces tenemos

df/dx = (24 (3 x² + 7) (4 x - 2)⁵ - 6 x (4 x - 2)⁶) / (3 x² + 7)²

Puedes parar aquí, o se puede simplificar el resultado un poco:

24 (3 x² + 7) (4 x - 2)⁵ - 6 x (4 x - 2)⁶

= (4 x - 2)⁵ (24 (3 x² + 7) - 6 x (4 x - 2))

= (4 x - 2)⁵ (48 x² + 12 x + 168)

Terminamos con

df/dx = (4 x - 2)⁵ (48 x² + 12 x + 168) / (3 x² + 7)²

the answer is 3,600,000 cubic centimeters

step-by-step explanation:

first you have to convert all the units into centimeters

2 meters = 200 centimeters

1.5 meters = 150 centimeters

to find the volume of a rectangular prism you multiply all the sides

120 * 200 * 150 = 3,600,000

the answer is 3,600,000 cubic centimeters

hope this !

the answer to the expression is 83