demonelite123
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Let g(t) = f(tx, ty).
Using the chain rule, we get g'(t) = (\frac{\partial f}{\partial x})(tx, ty) * x + (\frac{\partial f}{\partial y})(tx, ty) * y
this was actually part of a proof and what i don't understand is that why didn't they write (\frac{\partial f}{\partial (tx)}) and (\frac{\partial f}{\partial (ty)})? i know that the factors of x and y come from (\frac{\partial (tx)}{\partial t}) and (\frac{\partial (ty)}{\partial t}) respectively, but why aren't the other 2 partial derivatives with respect to tx and ty? what happened to the t's?
Using the chain rule, we get g'(t) = (\frac{\partial f}{\partial x})(tx, ty) * x + (\frac{\partial f}{\partial y})(tx, ty) * y
this was actually part of a proof and what i don't understand is that why didn't they write (\frac{\partial f}{\partial (tx)}) and (\frac{\partial f}{\partial (ty)})? i know that the factors of x and y come from (\frac{\partial (tx)}{\partial t}) and (\frac{\partial (ty)}{\partial t}) respectively, but why aren't the other 2 partial derivatives with respect to tx and ty? what happened to the t's?