Differentiation Question 273
Question: $ \frac{d}{dx}[ \log \sqrt{\sin \sqrt{e^{x}}} ] $ =
Options:
A) $ \frac{1}{4}{e^{x/2}}\cot ({e^{x/2}}) $
B) $ {e^{x/2}}\cot ({e^{x/2}}) $
C) $ \frac{1}{4}e^{x}\cot (e^{x}) $
D) $ \frac{1}{2}{e^{x/2}}\cot ({e^{x/2}}) $
Show Answer
Answer:
Correct Answer: A
Solution:
$ \frac{d}{dx}[\log \sqrt{\sin \sqrt{e^{x}}}]=\frac{d}{dx}[ \frac{1}{2}\log (\sin \sqrt{e^{x}}) ] $
$ =\frac{1}{2}\cot \sqrt{e^{x}}\frac{1}{2\sqrt{e^{x}}}e^{x}=\frac{1}{4}{e^{x/2}}\cot ({e^{x/2}}) $
BETA
