Derivative of y=2x^5+6x^2+9

1. Differentiate $\left(2 x^{5} + 6 x^{2}\right) + 9$ term by term:

   1. Differentiate $2 x^{5} + 6 x^{2}$ 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: $x^{5}$ goes to $5 x^{4}$

         So, the result is: $10 x^{4}$

      2. 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: $12 x$

      The result is: $10 x^{4} + 12 x$

   2. The derivative of the constant $9$ is zero.

   The result is: $10 x^{4} + 12 x$

The answer is:

$$10 x^{4} + 12 x$$