Differentiating a position function using linearity rules

Apply the sum/difference rule to differentiate each term of $s(t) = -16t^2 + 20t + 5$ separately: $s'(t) = \frac{d}{dt}[-16t^2] + \frac{d}{dt}[20t] + \frac{d}{dt}[5]$.

Using the constant multiple rule with the power rule, $\frac{d}{dt}[-16t^2] = -16(2t) = -32t$ and $\frac{d}{dt}[20t] = 20(1) = 20$. The derivative of the constant $5$ is $0$ by the constant rule, so combining these gives $s'(t) = -32t + 20$.