Question

If $y=e^{(1+{\log }_{e}x)}$ then find $\frac{dy}{dx}$.

Answer 1

Given,

$y=e^{(1+{\log }_{e}x)}$

or, $y=e.e^{{\log }_{e}x}$

or, $y=ex$. [ Since $e^{{\log }_{e}x}=x$].

Now differentiating both sides with respect to $x$ we get $\frac{dy}{dx}=e$.