Answer
See explanations.
Work Step by Step
Step 1. Recall the Derivative Product Rule as $\frac{d}{dx}(uv)=u\frac{dv}{dx}+v\frac{du}{dx}$ and letting $v=c$, we have
$\frac{d}{dx}(uc)=u\frac{dc}{dx}+c\frac{du}{dx}=0+c\frac{du}{dx}$ or $\frac{d}{dx}(cu)=c\frac{du}{dx}$
Step 2. Recall the Derivative Constant Multiple Rule as $\frac{d}{dx}(cu)=c\frac{du}{dx}$ and we can find that this is the same as the result from step-1.
Step 3. We can say that when a function is a constant in the the Derivative Product Rule, the formula will be reduced to that of the Derivative Constant Multiple Rule.
