A) \[({{x}^{2}}){{3}^{{{x}^{2}}-1}}\]
B) \[3{{x}^{2}}.2x\]
C) \[{{3}^{{{x}^{2}}}}.2x.\log 3\]
D) \[({{x}^{2}}-1).3\]
Correct Answer: C
Solution :
Given \[y={{3}^{{{x}^{2}}}}\] \[\because \frac{d}{dx}({{a}^{x}})={{a}^{x}}{{\log }_{e}}a\] \[\therefore \frac{dy}{dx}={{3}^{{{x}^{2}}}}{{\log }_{e}}3\frac{d}{dx}({{x}^{2}})\]Þ \[\frac{dy}{dx}={{3}^{{{x}^{2}}}}.2x.{{\log }_{e}}3\] .
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