Differentiation Question 404
Question: If $ y=a^{x}.{b^{2x-1}} $ , then $ \frac{d^{2}y}{dx^{2}} $ is
[Kerala (Engg.) 2005]
Options:
A) $ y^{2}.\log ab^{2} $
B) $ y.\log ab^{2} $
C) $ y^{2} $
D) $ y.{{(\log a^{2}b)}^{2}} $
E) $ y.{{(\log ab^{2})}^{2}} $
Show Answer
Answer:
Correct Answer: E
Solution:
$ y=a^{x}{b^{2x-1}} $
$ \frac{dy}{dx}=a^{x}{b^{2x-1}}\log a+2a^{x}{b^{2x-1}}\log b $
= $ a^{x}{b^{2x-1}}(\log a+2\log b) $
$ \frac{d^{2}y}{dx^{2}}=a^{x}{b^{2x-1}}{{(\log a+2\log b)}^{2}} $
$ =a^{x}{b^{2x-1}}{{(\log ab^{2})}^{2}} $
$ =y{{(\log ab^{2})}^{2}} $ .
BETA
