If we have a general function of the form:
$f(zx,zy)$ where $x,y,z$ are variables, what is the partial derivative of function $f$ with respect to $z$ in this case?
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1By $zx$ here do you mean the product of $z$ and $x$? – MJD Jun 09 '14 at 18:42
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Unclear what you are asking. Do you need an expression for $$\frac{d}{dz}f(zx,zy)?$$ – Yiorgos S. Smyrlis Jun 09 '14 at 18:43
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1Do you mean $f(x,y)$ where $x$ is a function of $z$ and y is also a function of $z$? – Mr Croutini Jun 09 '14 at 18:43
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Yep! It is the product of z and x. – user90831 Jun 09 '14 at 18:43
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@user90831, do you mean yes to Mr Croutini's statement? Because then the answer is different. – Christopher K Jun 09 '14 at 18:45
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Hi, sorry i was assuming that x,y,z are independent. But xz refers to the product of x and z here. – user90831 Jun 09 '14 at 18:47
1 Answers
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I presume that $x$,$y$ and $z$ are independent variables.
If so, the answer is quite simply $D_{1}f\cdot \frac{\partial (zx)}{\partial z} + D_{2}f\cdot \frac{\partial (zy)}{\partial z} = x\cdot D_{1} + y\cdot D_{2}$.
Christopher K
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