Differentiation Question 306
Question: If $ y={\log_2}[{\log_2}(x)] $ , then $ \frac{dy}{dx} $ is equal to
Options:
A) $ \frac{{\log_2}e}{x{\log _{e}}x} $
B) $ \frac{1}{{\log _{e}}x{\log _{e}}2} $
C) $ \frac{1}{{\log _{e}}{{(2x)}^{x}}} $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
$ y={\log_2}[{\log_2}(x)]={\log _{e}}({\log _{e}}x.{\log_2}e).{\log_2}e $
$ =[{\log _{e}}{\log _{e}}x+{\log _{e}}({\log_2}e)]{\log_2}e $
$ \therefore \frac{dy}{dx}={\log_2}e.\frac{1}{x{\log _{e}}x} $ .
BETA
