Is there a general formula for (total) derivatives of functions of the form [itex]f(xy(x)+z(x)[/itex]?(adsbygoogle = window.adsbygoogle || []).push({});

I tried the most simple function of that form [itex]f(xy(x)+z(x))=xy(x)+z(x)[/itex] and the formula I got was [itex]\frac{\partial f}{\partial x}+\frac{\partial f}{\partial y} \frac{dy}{dx}+\frac{\partial f}{\partial z}\frac{dz}{dx}[/itex] though I'm unsure if it's even close to what I'm after. The formula Mathematica gave is [itex]y\frac{\partial f}{\partial x}+x\frac{\partial f}{\partial y} \frac{dy}{dx}+\frac{\partial f}{\partial z}\frac{dz}{dx}[/itex]

Thanks

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# Derivatives of functions of products of variables

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