Derivative of y=x^2e^3x

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

   1. Apply the product rule:

      $$\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$$

      $f{\left(x \right)} = x$; to find $\frac{d}{d x} f{\left(x \right)}$:

      1. Apply the power rule: $x$ goes to $1$

      $g{\left(x \right)} = x^{2}$; to find $\frac{d}{d x} g{\left(x \right)}$:

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

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

   So, the result is: $3 x^{2} e^{3}$

The answer is:

$$3 x^{2} e^{3}$$