Differentiation Question 460
Question: $ \frac{d}{dx}{{{(\sin x)}^{x}}} $ =
[DSSE 1985, 87; AISSE 1983]
Options:
A) $ [ \frac{x\cos x+\sin x\log \sin x}{\sin x} ] $
B) $ {{(\sin x)}^{x}}[ \frac{x\cos x+\sin x\log \sin x}{\sin x} ] $
C) $ {{(\sin x)}^{x}}[ \frac{x\sin x+\sin x\log \sin x}{\sin x} ] $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
Let $ y={{(\sin x)}^{x}}\Rightarrow {\log _{e}}y=x{\log _{e}}\sin x $
$ \Rightarrow \frac{dy}{dx}={{(\sin x)}^{x}}[x\cot x+{\log _{e}}\sin x] $
$ ={{(\sin x)}^{x}}[ \frac{x\cos x+\sin x\log \sin x}{\sin x} ] $ .
BETA
