![]() ![]() 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.
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