Derivative of y=x³+4x²+6

1. Differentiate $x^{3} + 4 x^{2} + 6$ term by term:

   1. Apply the power rule: $x^{3}$ goes to $3 x^{2}$

   2. The derivative of a constant times a function is the constant times the derivative of the function.

      1. Apply the power rule: $x^{2}$ goes to $2 x$

      So, the result is: $8 x$

   3. The derivative of the constant $6$ is zero.

   The result is: $3 x^{2} + 8 x$

2. Now simplify:

   $$x \left(3 x + 8\right)$$

The answer is:

$$x \left(3 x + 8\right)$$