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Prove that: $$\frac{\partial x^*(p,r,w)}{\partial r }< 0$$

I plug x* into my equation, yielding: $$ \frac{pf'(x^*(p,r,w)}{1+r} - w = 0$$

Then applying the derivative: $$\frac{\partial}{\partial r} \frac{pf'(x^*(p,r,w)}{1+r} - \frac{\partial}{\partial r} w = 0 $$

How do I prove from here? Given $w>0, p>0, r>0, x>0$

Function: $$max (x;p,r,w) =\frac{pf(x)}{1+r} - wx$$

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    I feel like we need more information here. What function is f? Are w and p functions or constants? – 2017-02-26
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    I included the function. p and w are constants – 2017-02-26

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