Derivative of 4e^x-2xe^x-4

1. Differentiate $\left(- e^{x} 2 x + 4 e^{x}\right) - 4$ term by term:

   1. Differentiate $- e^{x} 2 x + 4 e^{x}$ term by term:

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

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

         So, the result is: $4 e^{x}$

      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 $1$

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

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

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

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

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

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

   2. The derivative of the constant $-4$ is zero.

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

2. Now simplify:

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

The answer is:

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