Interpretation of changing the inputs of the partial differentation of a function

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Let's say I have a function like this:

$$y=\frac{a(1-b/c)}{d-b}$$

and take the partial derivative w.r.t $c$ to get:

$$ \frac{\partial y}{\partial c} = \frac{a*b/c^2}{d-b} $$

What's the interpretation if I increase $c$? Is $y$ increasing or decreasing w.r.t $c$?

Now I take the partial derviative w.r.t $b$ to get: $$ \frac{\partial y}{\partial b} = \frac{a*(1-d/c)}{(d-b)^2} $$

What's the interpretation if I increase $b$? Is $y$ increasing or decreasing w.r.t $b$?

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Note that $$ \frac{\partial y}{\partial c} = \frac{ab}{d-b} \times \frac{1}{c^2}. $$ Hence, if $ab/(d-b) < 0$ then increasing $c$ decreases $1/c^2$ which increases $y$.

Alternatively, if $ab/(d-b) > 0$, then increasing $c$ decreases $1/c^2$ which decreases $y$.

Finally, if $a=0$ or $b=0$, then changing $c$ has no effect on $y$ whatsoever.

Can you yourself do the analysis of sensitivity to $b$?