1. The problem is to find the derivative of the denominator if the denominator is $1 + t$. 2. The derivative of a function $f(t)$ with respect to $t$ is denoted as $\frac{d}{dt}f(t)$. 3. Here, the denominator is $1 + t$, which is a sum of two terms: a constant $1$ and a variable $t$. 4. The derivative of a constant is $0$, and the derivative of $t$ with respect to $t$ is $1$. 5. Therefore, the derivative of the denominator $1 + t$ is: $$\frac{d}{dt}(1 + t) = \frac{d}{dt}(1) + \frac{d}{dt}(t) = 0 + 1 = 1$$ 6. So, the derivative of the denominator $1 + t$ is $1$.