Given y= e2 xx2 + 1, find dydx. Hence find its value at x=0. Show that the derivative is positive fo

Question

Given y= e2 xx2 + 1, find dydx. Hence find its value at x=0. Show that the derivative is positive for every real input.

Accepted Answer

$\dfrac{\mathrm{d}y}{\mathrm{d}x}=- \dfrac{2 x e^{2 x}}{\left(x^{2} + 1\right)^{2}} + \dfrac{2 e^{2 x}}{x^{2} + 1}$; at $x=0$, $2$. The derivative is positive for all real $x$.

Quotients of functions

Quotients of functions

Solution:

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