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in this video were going to derive the pullback or vector Jacobian product rule for non-linear system solving non-linear system solving or dissolution of high dimensional route finding problems can be seen as a function that takes an input here called Theta and then solves a zero condition for its roots thereby for instance applies or most commonly applies a newton-raphson method to obtain the root of that parameterized zero condition you will find these kind of nonlinear systems in scientific Computing so if you solve non-linear partial differential equations so for instance the navier Stokes equations you will also find them in non-linear optimization problems as well as more recently in deep equivalent models as part of deep learning in this video we want to look at pullback or vector Jacobian product rules because we have that computation the solution to nonlinear system solvings is part of a larger computational chain for which we then want to apply reverse mode automatic differ