Differentiation Question 450
Question: If $ y={{(x^{x})}^{x}} $ , then $ \frac{dy}{dx} $ =
Options:
A) $ {{(x^{x})}^{x}}(1+2\log x) $
B) $ {{(x^{x})}^{x}}(1+\log x) $
C) $ x{{(x^{x})}^{x}}(1+2\log x) $
D) $ x{{(x^{x})}^{x}}(1+\log x) $
Show Answer
Answer:
Correct Answer: C
Solution:
$ y={{(x^{x})}^{x}}\Rightarrow {\log _{e}}y=x{\log _{e}}{{(x)}^{x}} $ = $ x^{2}.{\log _{e}}x $
Therefore $ \frac{1}{y}\frac{dy}{dx} $ = $ x^{2}.\frac{1}{x}+2x.{\log _{e}}x $
$ \therefore \frac{dy}{dx}=x{{(x^{x})}^{x}}[1+2{\log _{e}}x] $ .
BETA
