Derivative of f(x)=5x³+2x

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

      So, the result is: $15 x^{2}$

   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: $2$

   The result is: $15 x^{2} + 2$

The answer is:

$$15 x^{2} + 2$$