JuliaDiff – Julia packages for automatic differentiation

Quote: "One option is to explicitly write down a function which computes the exact derivatives by using the rules that we know from Calculus. However, this quickly becomes an error-prone and tedious exercise."

There's the alternative of algorithmic symbolic differentiation. For most well-behaved functions, symbolic differentiation produces useful results (not true for the reverse case of symbolic integration). Many readily available libraries now produce symbolic differentiation and other similar results. Users should not dismiss this approach out of hand.