Differentiation Question 15
Question: The derivative of $ y={x^{\ln x}} $ is
[AMU 2000]
Options:
A) $ {x^{\ln x}}\ln x $
B) $ {x^{lnx-1}}lnx $
C) $ 2{x^{\ln x-1}}\ln x $
D) $ {x^{\ln x-2}} $
Show Answer
Answer:
Correct Answer: C
Solution:
$ y={x^{\ln x}} $
Therefore $ \ln y={{(\ln x)}^{2}} $
Therefore $ \frac{1}{y}\frac{dy}{dx}=\frac{2\ln x}{x} $
Therefore $ \frac{dy}{dx}=y\frac{2\ln x}{x}=\frac{2({x^{\ln x}})\ln x}{x} $
Therefore $ \frac{dy}{dx}=2{x^{\ln x-1}}\ln x $ .
BETA
