Two terms appear on the right-hand side of the formula, and f f is a function of two variables. The variables x and y x and y that disappear in this simplification are often called intermediate variables: they are independent variables for the function f, f, but are dependent variables for the variable t. If we treat these derivatives as fractions, then each product “simplifies” to something resembling ∂ f / d t. Recall that when multiplying fractions, cancelation can be used. The first term in the equation is ∂ f ∂ x This proves the chain rule at t = t 0 t = t 0 the rest of the theorem follows from the assumption that all functions are differentiable over their entire domains.Ĭloser examination of Equation 4.29 reveals an interesting pattern. Since x ( t ) x ( t ) and y ( t ) y ( t ) are both differentiable functions of t, t, both limits inside the last radical exist.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |