Derivative of 3x²+2x³

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

   1. 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: $6 x$

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

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

      So, the result is: $6 x^{2}$

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

2. Now simplify:

   $$6 x \left(x + 1\right)$$

The answer is:

$$6 x \left(x + 1\right)$$