A) \[{{e}^{{{x}^{3}}}}\]
B) \[3{{x}^{2}}{{e}^{{{x}^{3}}}}\]
C) \[3{{x}^{3}}{{e}^{{{x}^{3}}}}\]
D) \[3{{x}^{2}}{{e}^{{{x}^{3}}}}+3{{x}^{2}}\]
Correct Answer: C
Solution :
\[y={{e}^{{{x}^{3}}}}\], \[z=\log x\] Þ \[\frac{dy}{dx}={{e}^{{{x}^{3}}}}\,.\,(3{{x}^{2}})=3{{x}^{2}}{{e}^{{{x}^{3}}}}\] .....(i) and \[\frac{dz}{dx}=\frac{1}{x}\] ....(ii) Þ \[\frac{dy}{dz}=\frac{3{{x}^{2}}{{e}^{{{x}^{3}}}}}{\left( 1/x \right)}=3{{x}^{3}}{{e}^{{{x}^{3}}}}\].
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