Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

De afgeleide van $\boldsymbol{-\,\frac {1} {x^2} }$ is gelijk aan	A. $\large\boldsymbol{0}$
	B. $\large\boldsymbol{\frac {2} {x^3} }$
	C. $\large\boldsymbol{\frac {1} {x^4} }$
	D. $\large\boldsymbol{\frac {2} {x^4} }$
	E. $\large\boldsymbol{\frac {1} {2x^5} }$

[ 6-0726 - op net sinds 6.12.15-()-15.11.2024 ]

Translation in E N G L I S H

The derivative ofn $\boldsymbol{-\,\frac {1} {x^2} }$ is equal to	A. $\large\boldsymbol{0}$
	B. $\large\boldsymbol{\frac {2} {x^3} }$
	C. $\large\boldsymbol{\frac {1} {x^4} }$
	D. $\large\boldsymbol{\frac {2} {x^4} }$
	E. $\large\boldsymbol{\frac {1} {2x^5} }$

Oplossing - Solution

1^ste manier :
$\textbf{D}\left(-\frac{1}{x^2}\right)=-\textbf{D}\frac{1}{x^2}=-\left(-\frac{1}{x^4}\right).\textbf{D}x^2=\frac{\textbf{D}x^2}{x^4}=\frac{2x}{x^4}=\frac{2}{x^3}$
2^de manier :
$\textbf{D}\left(-\frac{1}{x^2}\right)=-\textbf{D}\frac{1}{x^2}=-\textbf{D}x^{-2}=-(-2)x^{-3}=\frac{2}{x^3}$
3^de manier :
$\textbf{D}\left(-\frac{1}{x^2}\right)=-\textbf{D}\left(\frac1x.\frac1x\right)=-\left(-\frac{1}{x^2}.\frac1x+\frac1x(-\frac{1}{x^2})\right)=\frac{1}{x^3}+\frac{1}{x^3}=\frac{2}{x^3}$

De afgeleide van \(\boldsymbol{-\,\frac {1} {x^2} }\) is gelijk aan	A. \(\large\boldsymbol{0}\)
	B. \(\large\boldsymbol{\frac {2} {x^3} }\)
	C. \(\large\boldsymbol{\frac {1} {x^4} }\)
	D. \(\large\boldsymbol{\frac {2} {x^4} }\)
	E. \(\large\boldsymbol{\frac {1} {2x^5} }\)

The derivative ofn \(\boldsymbol{-\,\frac {1} {x^2} }\) is equal to	A. \(\large\boldsymbol{0}\)
	B. \(\large\boldsymbol{\frac {2} {x^3} }\)
	C. \(\large\boldsymbol{\frac {1} {x^4} }\)
	D. \(\large\boldsymbol{\frac {2} {x^4} }\)
	E. \(\large\boldsymbol{\frac {1} {2x^5} }\)