Differentiation Question 310
Question: The differential of $ {e^{x^{3}}} $ with respect to $ \log x $ is
[Karnataka CET 2002]
Options:
A) $ {e^{x^{3}}} $
B) $ 3x^{2}{e^{x^{3}}} $
C) $ 3x^{3}{e^{x^{3}}} $
D) $ 3x^{2}{e^{x^{3}}}+3x^{2} $
Show Answer
Answer:
Correct Answer: C
Solution:
$ y={e^{x^{3}}} $ , $ z=\log x $
Therefore $ \frac{dy}{dx}={e^{x^{3}}}.(3x^{2})=3x^{2}{e^{x^{3}}} $ …..(i) and $ \frac{dz}{dx}=\frac{1}{x} $ ….(ii)
Therefore $ \frac{dy}{dz}=\frac{3x^{2}{e^{x^{3}}}}{( 1/x )}=3x^{3}{e^{x^{3}}} $ .
BETA
