Differentiation is the process of determining the rate of change of a function, \(f(x)\) with respect to an input, usually \(x\). 

HOW TO DIFFERENTIATE
\(\displaystyle {d\over dx}\) is the differential operator which indicates that we are differentiating with respect to \(x\). 
\(dy\over dx\) means that we are differentiating \(y\) with respect to \(x\).
\(dA\over dt\) means that we are differentiating \(A\) with respect to \(t\).
Alternately, for functions of the form \(y=f(x)\), \(dy\over dx\) can be written as \(f'(x)\) or \(y'\).
\({d\over dx}\: ax^n=nax^{n-1}\)