Derivative of 3x^2-5x+7

1. Differentiate $3 x^{2} - 5 x + 7$ 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: $x^{2}$ goes to $2 x$

      So, the result is: $6 x$

   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 power rule: $x$ goes to $1$

         So, the result is: $5$

      So, the result is: $-5$

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

   The result is: $6 x - 5$

The answer is:

$$6 x - 5$$