Derivative of y(x)=5x^3+2x^2+3x-1/2

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

      So, the result is: $4 x$

   3. 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: $3$

   4. The derivative of the constant $\left(-1\right) \frac{1}{2}$ is zero.

   The result is: $15 x^{2} + 4 x + 3$

The answer is:

$$15 x^{2} + 4 x + 3$$