Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

De afgeleide van $\boldsymbol{\frac {2x\,-\,1} {x} }$ is	A. 2
	B. $\boldsymbol{\frac {1} {x^2} }$
	C. $\boldsymbol{-\,\frac {1} {x^2} }$
	D. $\boldsymbol{\frac {2} {x^2} }$
	E. $\boldsymbol{-\,\frac {2} {x^2} }$

[ 4-0147 - op net sinds 16.4.05-(E)-30.10.2023 ]

Translation in E N G L I S H

The derivative of $\boldsymbol{\frac {2x\,-\,1} {x} }$ equals	A. 2
	B. $\boldsymbol{\frac {1} {x^2} }$
	C. $\boldsymbol{-\,\frac {1} {x^2} }$
	D. $\boldsymbol{\frac {2} {x^2} }$
	E. $\boldsymbol{-\,\frac {2} {x^2} }$

Oplossing - Solution

$\\ \text{Eerste manier :}\\ D\, \frac{2x-1}{x}=D\left ( \frac{2x}{x} \right )-D\frac{1}{x} =D\: 2 - \left ( -\frac{1}{x^2} \right )=0+\frac{1}{x^2}=\frac{1}{x^2}\\ \text{Tweede manier :}\\ D\, \frac{2x-1}{x}=\frac{D(2x-1).x-(2x-1).Dx}{x^2}=\frac{2.x-2x+1}{x^2}=\frac{1}{x^2}\\$

De afgeleide van \(\boldsymbol{\frac {2x\,-\,1} {x} }\) is	A. 2
	B. \(\boldsymbol{\frac {1} {x^2} }\)
	C. \(\boldsymbol{-\,\frac {1} {x^2} }\)
	D. \(\boldsymbol{\frac {2} {x^2} }\)
	E. \(\boldsymbol{-\,\frac {2} {x^2} }\)

The derivative of \(\boldsymbol{\frac {2x\,-\,1} {x} }\) equals	A. 2
	B. \(\boldsymbol{\frac {1} {x^2} }\)
	C. \(\boldsymbol{-\,\frac {1} {x^2} }\)
	D. \(\boldsymbol{\frac {2} {x^2} }\)
	E. \(\boldsymbol{-\,\frac {2} {x^2} }\)