Derivative of (5-3*x)*e^(2*x)

1. Apply the product rule:

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

   $f{\left(x \right)} = 5 - 3 x$; to find $\frac{d}{d x} f{\left(x \right)}$:

   1. Differentiate $5 - 3 x$ term by term:

      1. The derivative of the constant $5$ is zero.

      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 power rule: $x$ goes to $1$

            So, the result is: $3$

         So, the result is: $-3$

      The result is: $-3$

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

   1. Let $u = 2 x$.

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

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

      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: $2$

      The result of the chain rule is:

      $$2 e^{2 x}$$

   The result is: $2 \cdot \left(5 - 3 x\right) e^{2 x} - 3 e^{2 x}$

2. Now simplify:

   $$\left(7 - 6 x\right) e^{2 x}$$

The answer is: