Derivative of 6exp^x-3+7x

1. Differentiate $7 x + \left(6 e^{x} - 3\right)$ term by term:

   1. Differentiate $6 e^{x} - 3$ 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: $6 e^{x}$

      2. The derivative of the constant $-3$ is zero.

      The result is: $6 e^{x}$

   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: $7$

   The result is: $6 e^{x} + 7$

The answer is:

$$6 e^{x} + 7$$