Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$\text{De afgeleide van}\\\;\frac{x+3}{\sqrt{x^2+3}}\;\text{is gelijk aan} $	A. $\frac {x(x-1)} {(x^2+3)\sqrt{x^2+3}} $
	B. $\frac {3(1-x)} {\sqrt{x^2+3}} $
	C. $\frac {3(x+1)} {(x^2+3)\sqrt{x^2+3}} $
	D. $\frac {3(1-x)(x^3+3)} {\sqrt{x^2+3}} $
	E. $\frac {3(1-x)} {(x^2+3)\sqrt{x^2+3}} $

[ 5-1701 - op net sinds 21.5.98-(E)-29.1.2024 ]

Translation in E N G L I S H

$\text{The derivative of}\\\;\frac{x+3}{\sqrt{x^2+3}}\;\text{is equal to} $	A. $\frac {x(x-1)} {(x^2+3)\sqrt{x^2+3}} $
	B. $\frac {3(1-x)} {\sqrt{x^2+3}} $
	C. $\frac {3(x+1)} {(x^2+3)\sqrt{x^2+3}} $
	D. $\frac {3(1-x)(x^3+3)} {\sqrt{x^2+3}} $
	E. $\frac {3(1-x)} {(x^2+3)\sqrt{x^2+3}} $

Oplossing - Solution

$\\\textbf{D}\frac{x+3}{\sqrt{x^2+3}}\;=\frac{[\textbf{D}(x+3)].\sqrt{x^2+3}-(x+3).\textbf{D}\sqrt{x^2+3}}{x^2+3}=\frac{\sqrt{x^2+3}-(x+3).\frac{1}{2.\sqrt{x^2+3}}.2x}{x^3+3}\\=\frac{x^2+3-(x+3).x}{(x^2+3).\sqrt{x^2+3}}=\frac{x^2+3-x^2-3x}{(x^2+3).\sqrt{x^2+3}}=\frac{3(1-x)}{(x^2+3)\sqrt{x^2+3}}$

\(\text{De afgeleide van}\\\;\frac{x+3}{\sqrt{x^2+3}}\;\text{is gelijk aan} \)	A. \(\frac {x(x-1)} {(x^2+3)\sqrt{x^2+3}} \)
	B. \(\frac {3(1-x)} {\sqrt{x^2+3}} \)
	C. \(\frac {3(x+1)} {(x^2+3)\sqrt{x^2+3}} \)
	D. \(\frac {3(1-x)(x^3+3)} {\sqrt{x^2+3}} \)
	E. \(\frac {3(1-x)} {(x^2+3)\sqrt{x^2+3}} \)

\(\text{The derivative of}\\\;\frac{x+3}{\sqrt{x^2+3}}\;\text{is equal to} \)	A. \(\frac {x(x-1)} {(x^2+3)\sqrt{x^2+3}} \)
	B. \(\frac {3(1-x)} {\sqrt{x^2+3}} \)
	C. \(\frac {3(x+1)} {(x^2+3)\sqrt{x^2+3}} \)
	D. \(\frac {3(1-x)(x^3+3)} {\sqrt{x^2+3}} \)
	E. \(\frac {3(1-x)} {(x^2+3)\sqrt{x^2+3}} \)