Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

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

[ 5-0148 - op net sinds 19.7.12-(E)-9.7.2024 ]

Translation in E N G L I S H

The derivative of \(\frac{1}{x^2}\) is equal to	A. \(\large\boldsymbol{-\,\frac {1} {x^4} }\)
	B. \(\large\boldsymbol{-\,\frac {2} {x} }\)
	C. \(\large\boldsymbol{-\,\frac {2} {x^2} }\)
	D. \(\large\boldsymbol{-\,\frac {2} {x^3} }\)
	E. \(\large\boldsymbol{\frac {1} {2x} }\)

Oplossing - Solution

1^ste manier :
$D\frac{1}{x^2}=-\frac{1}{(x^2)^2}.Dx^2=-\frac{1}{x^4}.2x=-\frac{2}{x^3}$
2^de manier :
$D\frac{1}{x^2}=Dx^{-2}=-2.x^{-3}=-\frac{2}{x^3}$