A) \[\frac{2xy+{{\sec }^{2}}x+y\sec x\tan x}{{{x}^{2}}+\sec x}\]
B) \[-\frac{2xy+{{\sec }^{2}}x+\sec x\tan x}{{{x}^{2}}+\sec x}\]
C) \[-\frac{2xy+{{\sec }^{2}}x+y\sec x\tan x}{{{x}^{2}}+\sec x}\]
D) None of these
Correct Answer: C
Solution :
\[y\sec x+\tan x+{{x}^{2}}y=0\] \[\Rightarrow \sec x\frac{dy}{dx}+y\sec x\tan x+{{\sec }^{2}}x+2xy+{{x}^{2}}\frac{dy}{dx}=0\] Þ \[\frac{dy}{dx}=-\frac{2xy+{{\sec }^{2}}x+y\sec x\tan x}{{{x}^{2}}+\sec x}\].
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