1.

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

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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