A) \[-\tan ({{x}^{3}})\]
B) \[\tan ({{x}^{3}})\]
C) \[-cot({{x}^{3}})\]
D) \[cot({{x}^{3}})\]
Correct Answer: C
Solution :
Let \[u=\sin {{x}^{3}}\] and \[v=\cos {{x}^{3}}\]. On differentiating w.r.t. x, we get \[\frac{du}{dx}=\cos \,{{x}^{3}}.3{{x}^{2}}\] and \[\frac{dv}{dx}=-\sin {{x}^{3}}.3{{x}^{2}}\] \[\therefore \] \[\frac{du}{dv}=\frac{du/dx}{dv/dx}=\frac{3{{x}^{2}}\,\cos \,{{x}^{3}}}{-3{{x}^{2}}\,\sin {{x}^{3}}}=-\cot {{x}^{3}}\]You need to login to perform this action.
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