In some cases, the D* derivatives rival the best manually derived solutions. For the test suite problems D* generates symbolic derivatives which are up to 4.6ÃƒÆ’Ã¢â‚¬â€10^3 times faster than those computed by the symbolic math program Mathematica and up to 2.2ÃƒÆ’Ã¢â‚¬â€10^5 times faster than the non-symbolic automatic differentiation program CppAD. This graph has a sum of products form the new algorithm computes a factorization of this derivative graph along with an efficient grouping of product terms into subexpressions. The D* algorithm computes efficient symbolic derivatives for these functions by symbolically executing the expression graph at compile time to eliminate common subexpressions and by exploiting the special nature of the graph that represents the derivative of a function. It performs function on arrays of every dimension. It performs functions in two-dimensional array. Mathematica’s graphing capabilities are currently the SOTA. It provides feature to analyze the data into charts still, there is a chart variety order of magnitudes smaller than Mathematica’s. Functions with densely interconnected expression graphs, which arise in applications such as dynamics, spacetime optimization (also known as the optimal control problem), and PRT, can be difficult to efficiently differentiate using existing symbolic or automatic differentiation techniques. Mathematica is capable of performing complex queries. D* generates symbolic derivatives which can be thousands of times faster than those generated by Mathematica or automatic differentiation. The following module performs implicit differentiation of an equation of two variables in a conventional format, i.e., with independent variable of the form x (or some other symbol), and dependent variable of the form y (or some other symbol).

Differentiate mathematica