A) \[\frac{x\sin x+4\cos x}{{{x}^{5}}}\]
B) \[\frac{-(x\sin x+4\cos x)}{{{x}^{5}}}\]
C) \[\frac{4\cos x-x\sin x}{{{x}^{5}}}\]
D) None of these
Correct Answer: B
Solution :
\[\frac{d}{dx}\left( \frac{1}{{{x}^{4}}\sec x} \right)=\frac{d}{dx}\left( \frac{\cos x}{{{x}^{4}}} \right)\]\[=\frac{{{x}^{4}}(-\sin x)-\cos x(4{{x}^{3}})}{{{({{x}^{4}})}^{2}}}\] \[=\frac{-{{x}^{3}}(x\sin x+4\cos x)}{{{x}^{8}}}=\frac{-(x\sin x+4\cos x)}{{{x}^{5}}}\].
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