Derivative of x^3+3x^2+1

1. Differentiate $\left(x^{3} + 3 x^{2}\right) + 1$ term by term:

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

      The result is: $3 x^{2} + 6 x$

   2. The derivative of the constant $1$ is zero.

   The result is: $3 x^{2} + 6 x$

2. Now simplify:

   $$3 x \left(x + 2\right)$$

The answer is:

$$3 x \left(x + 2\right)$$