1. Why is the derived function of a function such as f(x) = c, where c is a constant, always 0.
Because f(x) = c is a horizontal straight line whose gradient is 0.
2. Is it possible to differentiate an expression with brackets in.
There are ways to differentiate with brackets still there but at this level it is simpler to expand them first.
3. Is it possible to differentiate every function?
Some parts of functions do not have a gradient.
e.g. In an absolute value function or a piecewise function if the graph is pointed, the gradient is not defined at that point.
If a particular function is not continuous i.e. You have to lift your pen off the paper when sketching the graph, it is not likely to have a gradient at that point.