Question 1111998
the definition of derivation is f'(x) = limit of (f(x+h) - f(x)) / h, as h approaches 0.


when f(x) = Ax + B, this becomes:


f'(x) = limit of (A(x+h) - B - (Ax + B) / h, as h approaches 0, which becomes:


f'(x) = limit of (Ax + Ah - B - Ax = B) / h, as h approaches 0.


Ax - Ax cancels out and B - B cancels out, so you are left with:


f'(x) = limit of Ah / h, as h approaches 0.


as long as h approaches 0, but is never 0, then h cancels out and you are left with:


f'(x) = A.


here's a reference on derivative of a function.


<a href = "http://web.mit.edu/wwmath/calculus/differentiation/definition.html" target = "_blank">http://web.mit.edu/wwmath/calculus/differentiation/definition.html</a>