Derivative of (2x^3-x)*exp^x

1. Apply the product rule:

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

   $f{\left(x \right)} = 2 x^{3} - x$; to find $\frac{d}{d x} f{\left(x \right)}$:

   1. Differentiate $2 x^{3} - x$ 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: $x^{3}$ goes to $3 x^{2}$

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

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

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

         So, the result is: $-1$

      The result is: $6 x^{2} - 1$

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

   1. The derivative of $e^{x}$ is itself.

   The result is: $\left(6 x^{2} - 1\right) e^{x} + \left(2 x^{3} - x\right) e^{x}$

2. Now simplify:

   $$\left(2 x^{3} + 6 x^{2} - x - 1\right) e^{x}$$

The answer is:

$$\left(2 x^{3} + 6 x^{2} - x - 1\right) e^{x}$$