Differentiation Question 194
Question: $ \frac{d}{dx}( \frac{1}{x^{4}\sec x} )= $
Options:
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
Show Answer
Answer:
Correct Answer: B
Solution:
$ \frac{d}{dx}( \frac{1}{x^{4}\sec x} )=\frac{d}{dx}( \frac{\cos x}{x^{4}} ) $
$ =\frac{x^{4}(-\sin x)-\cos x(4x^{3})}{{{(x^{4})}^{2}}} $
$ =\frac{-x^{3}(x\sin x+4\cos x)}{x^{8}}=\frac{-(x\sin x+4\cos x)}{x^{5}} $ .
BETA
