Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$https://latex.codecogs.com/png.image?\dpi{120}D^{10}\: \frac{1}{x+2}\; =$	A. $\boldsymbol{10}$
	B. $\boldsymbol{\frac {10\,!} {(x\,+\,2)^{10}} }$
	C. $\boldsymbol{-\,\frac {10\,!} {(x\,+\,2)^{10}} }$
	D. $\boldsymbol{\frac {10\,!} {(x\,+\,2)^{11}} } $
	E. $\boldsymbol{-\,\frac {10\,!} {(x\,+\,2)^{11}} }$

[ 5-7986 - op net sinds 10.12.15-()-31.12.2023 ]

Translation in E N G L I S H

IN CONSTRUCTION	A.
	B.
	C.
	D.
	E.

Oplossing - Solution

$\\\mathbf{D}^{10}\frac{1}{x+2}=\mathbf{D}^9\left(-\frac{1}{(x+2)^2}\right)=\mathbf{D}^8\left(\frac{2.(x+2)}{(x+2)^4}\right)=2.\mathbf{D}^8\left(\frac{1}{(x+2)^3}\right)\\=2.\mathbf{D}^7\left(-\frac{3(x+2)^2}{(x+2)^6}\right)=-2.3.\mathbf{D}^7\left(\frac{1}{(x+2)^4}\right)=-2.3.\mathbf{D}^6\left(\frac{4(x+2)^3}{(x+2)^8}\right)\\=+2.3.4.\mathbf{D}^6\left(\frac{1}{(x+2)^5}\right)=\cdots=2.3.4.5.6.7.8.9.10.\frac{1}{(x+2)^{11}}=\frac{10!}{(x+2)^{11}$

$https://latex.codecogs.com/png.image?\dpi{120}D^{10}\: \frac{1}{x+2}\; =$	A. \(\boldsymbol{10}\)
	B. \(\boldsymbol{\frac {10\,!} {(x\,+\,2)^{10}} }\)
	C. \(\boldsymbol{-\,\frac {10\,!} {(x\,+\,2)^{10}} }\)
	D. \(\boldsymbol{\frac {10\,!} {(x\,+\,2)^{11}} } \)
	E. \(\boldsymbol{-\,\frac {10\,!} {(x\,+\,2)^{11}} }\)