Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

De tweede orde afgeleide van $\frac{1+x}{1-x}$ is gelijk aan	A. $\boldsymbol{\frac {4} {(1\,-\,x)^3} }$
	B. $\boldsymbol{\frac {2} {(1\,-\,x)^4} }$
	C. $\boldsymbol{-\,\frac {4} {(1\,-\,x)^3} }$
	D. $\boldsymbol{\frac {4x} {(1\,-\,x)^4} }$
	E. $\boldsymbol{-\,\frac {4x} {(1\,-\,x)^4} }$

[ 4-4599 - op net sinds 27.6.07-(E)-2.11.2023 ]

Translation in E N G L I S H

The second order derivative of $https://latex.codecogs.com/png.image?\dpi{110}\frac{1+x}{1-x}$ is equal to	A. $\boldsymbol{\frac {4} {(1\,-\,x)^3} }$
	B. $\boldsymbol{\frac {2} {(1\,-\,x)^4} }$
	C. $\boldsymbol{-\,\frac {4} {(1\,-\,x)^3} }$
	D. $\boldsymbol{\frac {4x} {(1\,-\,x)^4} }$
	E. $\boldsymbol{-\,\frac {4x} {(1\,-\,x)^4} }$

Oplossing - Solution

$\\ \text{Eerste orde afgeleide :}\\ D\frac{1+x}{1-x}=\frac{1.(1-x)-(1+x)(-1)}{(1-x)^2}=\frac{1-x+1+x}{(1-x)^2}=\frac{2}{(1-x)^2}\\ \text{Tweede orde afgeleide :}\\ D\frac{2}{(1-x)^2}=2.D\frac{1}{(1-x)^2}=2.\left ( -\, \frac{2.(1-x)(-1)}{(1-x)^4} \right )=\frac{4}{(1-x)^3}$

De tweede orde afgeleide van $\frac{1+x}{1-x}$ is gelijk aan	A. \(\boldsymbol{\frac {4} {(1\,-\,x)^3} }\)
	B. \(\boldsymbol{\frac {2} {(1\,-\,x)^4} }\)
	C. \(\boldsymbol{-\,\frac {4} {(1\,-\,x)^3} }\)
	D. \(\boldsymbol{\frac {4x} {(1\,-\,x)^4} }\)
	E. \(\boldsymbol{-\,\frac {4x} {(1\,-\,x)^4} }\)

The second order derivative of $https://latex.codecogs.com/png.image?\dpi{110}\frac{1+x}{1-x}$ is equal to	A. \(\boldsymbol{\frac {4} {(1\,-\,x)^3} }\)
	B. \(\boldsymbol{\frac {2} {(1\,-\,x)^4} }\)
	C. \(\boldsymbol{-\,\frac {4} {(1\,-\,x)^3} }\)
	D. \(\boldsymbol{\frac {4x} {(1\,-\,x)^4} }\)
	E. \(\boldsymbol{-\,\frac {4x} {(1\,-\,x)^4} }\)