If $y=\sqrt{e^x+\sqrt{e^x+\sqrt{e^x+\ldots \infty}}}$ then $\frac{d y}{d x}$ is

Question

Professor PC Thomas Classes · Answer

Substituting infinite recurrence: $y^2 = e^x + y$. Implicit differentiation yields $2yy' = e^x + y' \Rightarrow y' = \frac{e^x}{2y-1}$.