Final answer to the problem
Step-by-step Solution
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Find the derivative of $0$ using the definition. Apply the definition of the derivative: $\displaystyle f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}$. The function $f(x)$ is the function we want to differentiate, which is $0$. Substituting $f(x+h)$ and $f(x)$ on the limit, we get
Add the values $0$ and $0$
Zero divided by anything is equal to zero
The limit of a constant is just the constant