Differentiation Question 462
Question: $ \frac{d}{dx}{{{(\sin x)}^{\log x}}}= $
[DSSE 1984]
Options:
A) $ {{(\sin x)}^{\log x}}[ \frac{1}{x}\log \sin x+\cot x ] $
B) $ {{(\sin x)}^{\log x}}[ \frac{1}{x}\log \sin x+\cot x\log x ] $
C) $ {{(\sin x)}^{\log x}}[ \frac{1}{x}\log \sin x+\log x ] $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
Let $ y={{(\sin x)}^{\log x}}\Rightarrow {\log _{e}}y={\log _{e}}x{\log _{e}}\sin x $
Therefore $ \frac{dy}{dx}={{(\sin x)}^{{\log _{e}}x}}=[ \frac{1}{x}{\log _{e}}\sin x+\cot x{\log _{e}}x ] $ .
BETA
