Simplifying differentiation with a constant

Question

I have a quick question. Take this:

d(C-x)/dt

Where C is a constant and x is a variable. Is there a way in which I can simplify that expression to get out of the bracket the constant?

Answer 1

I suppose that $x$ is a function of $t$, that is $x=x(t)$. Since the derivative is linear, you have that $$\frac{\text{d}}{\text{d}t}(C-x(t))=\frac{\text{d}}{\text{d}t}(C)-\frac{\text{d}}{\text{d}t}x(t)=0-x^\prime(t)=-x^\prime(t)$$ If $x$ is not a function of $t$, then both $C$ and $x$ are constants with respect of $t$ and so the derivative is $0$.