Differentiation Question 343
Question: If $ y={{\cos }^{-1}}( \frac{3\cos x+4\sin x}{5} ) $ , then $ \frac{dy}{dx}= $
Options:
A) 0
B) 1
C) $ -1 $
D) $ \frac{1}{2} $
Show Answer
Answer:
Correct Answer: B
Solution:
$ y={{\cos }^{-1}}[ \frac{3}{5}\cos x-\frac{4}{5}\sin x ] $
Putting $ \frac{3}{5}=r\cos \theta ,\frac{4}{5}=r\sin \theta \Rightarrow r=1 $
Therefore $ y={{\cos }^{-1}}[\cos \theta \cos x-\sin \theta \sin x]=\theta +x $
$ \Rightarrow \frac{dy}{dx}=1 $ .
BETA
