Consider the above Geogebra worksheet and try to answer the questions. You might find it difficult to visualise the result of adding or subtracting two functions in which case concentrate on answering the other questions. You can input new building blocks e.g. try f(x)=sin(x), g(x) = cos(x). What rules do the gradients obey? What does this suggest the rules might be for differentiating a sum or a difference of two functions?
