Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

De afgeleide $https://latex.codecogs.com/png.image?\inline \large \dpi{120}\textbf{D}\sqrt{x+\sqrt{x+\sqrt{x+\cdots }}}$ is gelijk aan	A. $\frac{1}{\sqrt{1+x}}$
	B. $\frac{1}{2\, \sqrt{1+x}}$
	C. $\frac{1}{\sqrt{1+2x}}$
	D. $\frac{1}{\sqrt{1+4x}}$
	E. $\frac{1}{2\, \sqrt{1+4x}}$

[ 5-8734 - op net sinds 15.4.2021-(E)-22.10.2026 ]

Translation in E N G L I S H

The derivative $https://latex.codecogs.com/png.image?\inline \large \dpi{120}\textbf{D}\sqrt{x+\sqrt{x+\sqrt{x+\cdots }}}$ is equal to	A. $\frac{1}{\sqrt{1+x}}$
	B. $\frac{1}{2\, \sqrt{1+x}}$
	C. $\frac{1}{\sqrt{1+2x}}$
	D. $\frac{1}{\sqrt{1+4x}}$
	E. $\frac{1}{2\, \sqrt{1+4x}}$

Oplossing - Solution

$Stel\;\;y=\sqrt{x+\sqrt{x+\sqrt{x+...}}}$
dan is y² = x + y (!)
en y² − y + x = 0
Discriminant is 1 + 4x.
$\large y=\frac{1+\sqrt{1+4x}}{2}$ ( y ≥ 0)
$\large D_x\;y=\frac12.\frac {1.4} {2.\sqrt{1+4x}}=\frac{1}{\sqrt{1+4x}} $

De afgeleide $https://latex.codecogs.com/png.image?\inline \large \dpi{120}\textbf{D}\sqrt{x+\sqrt{x+\sqrt{x+\cdots }}}$ is gelijk aan	A. \(\frac{1}{\sqrt{1+x}}\)
	B. \(\frac{1}{2\, \sqrt{1+x}}\)
	C. \(\frac{1}{\sqrt{1+2x}}\)
	D. \(\frac{1}{\sqrt{1+4x}}\)
	E. \(\frac{1}{2\, \sqrt{1+4x}}\)

The derivative $https://latex.codecogs.com/png.image?\inline \large \dpi{120}\textbf{D}\sqrt{x+\sqrt{x+\sqrt{x+\cdots }}}$ is equal to	A. \(\frac{1}{\sqrt{1+x}}\)
	B. \(\frac{1}{2\, \sqrt{1+x}}\)
	C. \(\frac{1}{\sqrt{1+2x}}\)
	D. \(\frac{1}{\sqrt{1+4x}}\)
	E. \(\frac{1}{2\, \sqrt{1+4x}}\)