If y = e^{(1 + log_e x)},then the value of fr | vedclass

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(A) Given the function $y = e^{(1 + \log_e x)}$.Using the property of exponents $a^{m+n} = a^m \cdot a^n$,we can rewrite the expression as:$y = e^1 \c

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$e$

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(A) Given the function $y = e^{(1 + \log_e x)}$.Using the property of exponents $a^{m+n} = a^m \cdot a^n$,we can rewrite the expression as:$y = e^1 \cdot e^{\log_e x}$Since $e^{\log_e x} = x$,the equation simplifies to:$y = e \cdot x$Now,differentiating $y$ with respect to $x$:$\frac{dy}{dx} = \frac{d}{dx}(ex)$Since $e$ is a constant,we get:$\frac{dy}{dx} = e \cdot \frac{d}{dx}(x) = e \cdot 1 = e$Therefore,the correct option is $A$.

If $y = e^{(1 + \log_e x)}$,then the value of $\frac{dy}{dx} = $

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