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Consider the curve `x=a(cos theta+thetasin theta)and y=a(sin theta-thetacos theta).` If `y=xln x+xe^(x)`, then what is the value of `(dy)/(dx)` at x = 1?A. `1+e`B. `1-e`C. `1+2e`D. None of these |
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Answer» Correct Answer - C `y = "x In x" + xe^(x)` After differentiating both sides with respect to x, we get `(dy)/(dx)=x.(1)/(x)+log x + xe^(x) + e^(x)` or `=1 + log x + xe^(x) + e^(x)` Therefore `((dy)/(dx))_(x=1)=1 + log 1 + 1.e^(1) + e^(1) = 1 = 2e" "[because log 1 = 0]` |
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