Derivative of y=xxx+2xx(2,3)

1. Differentiate $x x x + \frac{23 x 2 x}{10}$ term by term:

   1. Apply the product rule:

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

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

      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 $1$

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

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

         The result is: $2 x$

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

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

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

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

      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 $1$

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

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

            The result is: $2 x$

         So, the result is: $4 x$

      So, the result is: $\frac{46 x}{5}$

   The result is: $2 x^{2} + x x + \frac{46 x}{5}$

2. Now simplify:

   $$\frac{x \left(15 x + 46\right)}{5}$$

The answer is:

$$\frac{x \left(15 x + 46\right)}{5}$$