Derivative of (3*x-5)*(7-x)

1. Apply the product rule:

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

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

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

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

      The result is: $3$

   $g{\left(x \right)} = 7 - x$; to find $\frac{d}{d x} g{\left(x \right)}$:

   1. Differentiate $7 - x$ term by term:

      1. The derivative of the constant $7$ is zero.

      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: $-1$

   The result is: $26 - 6 x$

The answer is:

$$26 - 6 x$$