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Regarding derivatives, suppose we have some function ##f = y(t)x +x^2## where ##y## is an implicit function of ##t## and ##x## is independent of ##t##. Isn't the following true, regarding the difference between a partial and full derivative?

$$ \frac{df}{dt} = \frac{\partial f}{\partial t} + \frac{\partial f}{\partial y}\frac{dy}{d t} + \frac{\partial f}{\partial x}\frac{d x}{d t} = \frac{\partial f}{\partial y}\frac{dy}{d t}$$

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# I Partial and Full derivatives

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