Derivative of x^2*exp(0.4*x)-2

1. Differentiate $x^{2} e^{\frac{2 x}{5}} - 2$ term by term:

   1. Apply the product rule:

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

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

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

      $g{\left(x \right)} = e^{\frac{2 x}{5}}$; to find $\frac{d}{d x} g{\left(x \right)}$:

      1. Let $u = \frac{2 x}{5}$.

      2. The derivative of $e^{u}$ is itself.

      3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \frac{2 x}{5}$:

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

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

            So, the result is: $\frac{2}{5}$

         The result of the chain rule is:

         $$\frac{2 e^{\frac{2 x}{5}}}{5}$$

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

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

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

2. Now simplify:

   $$\frac{2 x \left(x + 5\right) e^{\frac{2 x}{5}}}{5}$$

The answer is:

$$\frac{2 x \left(x + 5\right) e^{\frac{2 x}{5}}}{5}$$