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 $b$?
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 $b$?