Differentiation Question 428
Question: If $ y=x^{x} $ , then $ \frac{dy}{dx}= $
[AISSE 1984; DSSE 1982; MNR 1979; SCRA 1996; RPET 1996; Kerala (Engg.) 2002]
Options:
A) $ x^{x}\log ex $
B) $ x^{x}( 1+\frac{1}{x} ) $
C) $ (1+\log x) $
D) $ x^{x}\log x $
Show Answer
Answer:
Correct Answer: A
Solution:
$ y=x^{x} $
Taking $ \log $ on both sides,
Therefore $ \log y=x\log x $
Differentiating with respect to x, we get
Therefore $ \frac{1}{y}\frac{dy}{dx}=1+\log x $ ;
$ \therefore \frac{dy}{dx}=x^{x}(1+\log x)=x^{x}\log ex $ .
BETA
