Differentiation Question 73
Question: $ \frac{d}{dx}\log \tan ( \frac{\pi }{4}+\frac{x}{2} )= $
Options:
A) $ \cos ecx $
B) $ -\cos ecx $
C) $ \sec x $
D) $ -\sec x $
Show Answer
Answer:
Correct Answer: C
Solution:
$ \frac{d}{dx}\log \tan ( \frac{\pi }{4}+\frac{x}{2} )=\frac{1}{\tan ( \frac{\pi }{4}+\frac{x}{2} )}{{\sec }^{2}}( \frac{\pi }{4}+\frac{x}{2} ).\frac{1}{2} $
$ =\frac{1}{2}.\frac{1}{\sin ( \frac{\pi }{4}+\frac{x}{2} )\cos ( \frac{\pi }{4}+\frac{x}{2} )}=\frac{1}{\sin ( \frac{\pi }{2}+x )}=\frac{1}{\cos x}=\sec x $ .
BETA
