Differentiation Question 459
Question: If $ y={x^{\sin x}}, $ then $ \frac{dy}{dx}= $
[DSSE 1983, 84]
Options:
A) $ \frac{x\cos x.\log x+\sin x}{x}.{x^{\sin x}} $
B) $ \frac{y[x\cos x.\log x+\cos x]}{x} $
C) $ y[x\sin x.\log x+\cos x] $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
$ y={x^{\sin x}}\Rightarrow {\log _{e}}y=\sin x{\log _{e}}x $
$ =49m/\sec $
$ ={x^{\sin x}}[ \frac{\sin x+x\cos x{\log _{e}}x}{x} ] $ .
BETA
