Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

De afgeleide D ln (log x) is gelijk aan	A. $\boldsymbol{1}$
	B. $\large\boldsymbol{\frac {1} {\log x} }$
	C. $\large\boldsymbol{\frac {1} {x.\log x} }$
	D. $\large\boldsymbol{\frac {1} {x.\ln x} }$
	E. $\large\boldsymbol{\frac {1} {x.\ln x.\log x} }$

[ 6-4191 - op net sinds 24.10.12-(E)-3.11.2023 ]

Translation in E N G L I S H

The derivative D ln (log x) is equal to	A. $\boldsymbol{1}$
	B. $\large\boldsymbol{\frac {1} {\log x} }$
	C. $\large\boldsymbol{\frac {1} {x.\log x} }$
	D. $\large\boldsymbol{\frac {1} {x.\ln x} }$
	E. $\large\boldsymbol{\frac {1} {x.\ln x.\log x} }$

Oplossing - Solution

$https://latex.codecogs.com/png.image?\dpi{110}\\D\ln(\log x)=\frac{1}{\log x}.D\log x=\frac{1}{\log x}.\frac{1}{x.\ln 10}=\frac{1}{x.\ln 10.\log x}=\frac{1}{x.\ln x}\\In\;de\;laatste\;stap\;hebben\;we\;gebruik\;gemaakt\;van\;de\;formule\\\log_a b.\log_b c = \log_a c$

De afgeleide D ln (log x) is gelijk aan	A. \(\boldsymbol{1}\)
	B. \(\large\boldsymbol{\frac {1} {\log x} }\)
	C. \(\large\boldsymbol{\frac {1} {x.\log x} }\)
	D. \(\large\boldsymbol{\frac {1} {x.\ln x} }\)
	E. \(\large\boldsymbol{\frac {1} {x.\ln x.\log x} }\)

The derivative D ln (log x) is equal to	A. \(\boldsymbol{1}\)
	B. \(\large\boldsymbol{\frac {1} {\log x} }\)
	C. \(\large\boldsymbol{\frac {1} {x.\log x} }\)
	D. \(\large\boldsymbol{\frac {1} {x.\ln x} }\)
	E. \(\large\boldsymbol{\frac {1} {x.\ln x.\log x} }\)