A) \[4\]
B) \[-3\]
C) \[-4\]
D) \[3\]
Correct Answer: C
Solution :
\[\sqrt{x}+\sqrt{y}=10\] \[\frac{1}{2\sqrt{x}}\frac{dx}{dy}+\frac{1}{2\sqrt{y}}=0\] \[\Rightarrow \] \[\frac{dx}{dy}=-\frac{\sqrt{x}}{\sqrt{y}}=-\frac{10-\sqrt{y}}{\sqrt{y}}\] \[\Rightarrow \] \[\frac{dx}{dy}=\frac{\sqrt{y}-10}{\sqrt{y}}\] \[\Rightarrow \] \[{{\left( \frac{dy}{dx} \right)}_{y=4}}=\frac{2-10}{2}=\frac{-8}{2}=-4\]
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