Derivative of y=(7x+5)*(x-4)

1. Apply the product rule:

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

   $f{\left(x \right)} = 7 x + 5$; to find $\frac{d}{d x} f{\left(x \right)}$:

   1. Differentiate $7 x + 5$ 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: $x$ goes to $1$

         So, the result is: $7$

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

      The result is: $7$

   $g{\left(x \right)} = x - 4$; to find $\frac{d}{d x} g{\left(x \right)}$:

   1. Differentiate $x - 4$ term by term:

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

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

      The result is: $1$

   The result is: $14 x - 23$

The answer is:

$$14 x - 23$$