Derivative of 3t^2-5t+6

1. Differentiate $\left(3 t^{2} - 5 t\right) + 6$ term by term:

   1. Differentiate $3 t^{2} - 5 t$ 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: $t^{2}$ goes to $2 t$

         So, the result is: $6 t$

      2. The derivative of a constant times a function is the constant times the derivative of the function.

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

         So, the result is: $-5$

      The result is: $6 t - 5$

   2. The derivative of the constant $6$ is zero.

   The result is: $6 t - 5$

The answer is:

$$6 t - 5$$