A) \[{{e}^{{{x}^{3}}}}\]
B) \[3{{x}^{2}}\,2{{e}^{{{x}^{3}}}}\]
C) \[3{{x}^{3}}{{e}^{{{x}^{3}}}}\]
D) \[3{{x}^{2}}{{e}^{{{x}^{3}}}}+3x\]
Correct Answer: C
Solution :
Let \[y={{e}^{{{x}^{3}}}},\,z=\log \,x\] Differentiating w.r.t x, we get \[\frac{dy}{dx}={{e}^{{{x}^{3}}}}\left( 3{{x}^{2}} \right)=3{{x}^{2}}{{e}^{{{x}^{3}}}}\] and \[\frac{dz}{dx}=\frac{1}{x}\] \[\therefore \,\,\frac{dy}{dx}=\frac{\frac{dy}{dx}}{\frac{dz}{dx}}=\frac{3{{x}^{2}}{{e}^{{{x}^{3}}}}}{\left( \frac{1}{x} \right)}=3{{x}^{3}}{{e}^{{{x}^{3}}}}\]
You need to login to perform this action.
You will be redirected in
3 sec
