Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

De afgeleide van $\ln \frac 1x$ is gelijk aan	A. \(\large\boldsymbol{-\,\frac {1} {x} }\)
	B. \(\large\boldsymbol{-\,\frac {1} {x^2} }\)
	C. \(\boldsymbol{x}\)
	D. \(\large\boldsymbol{\frac {1} {\ln x} }\)
	E. \(\large\boldsymbol{\frac {1} {x} }\)
	F. \(\boldsymbol{0 }\)

[ 6-0631 - op net sinds 16.2.13-(E)-30.10.2023 ]

Translation in E N G L I S H

The derivative of $\ln \frac 1x$ is equal to	A. \(\large\boldsymbol{-\,\frac {1} {x} }\)
	B. \(\large\boldsymbol{-\,\frac {1} {x^2} }\)
	C. \(\boldsymbol{x}\)
	D. \(\large\boldsymbol{\frac {1} {\ln x} }\)
	E. \(\large\boldsymbol{\frac {1} {x} }\)
	F. \(\boldsymbol{0 }\)

Oplossing - Solution

$\large \color{DarkGreen} { D\; ln\frac{1}{x}= \frac{1}{\frac{1}{x}}\cdot D\; \frac{1}{x}= x\cdot (-\frac{1}{x^2})= -\frac{1}{x} }$