Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

De afgeleide van \(\boldsymbol{ \frac {1} {\sqrt x} }\) is gelijk aan	A. \(\boldsymbol{ 2\,\sqrt x}\)
	B. \(\boldsymbol{ -\,2\,\sqrt x}\)
	C. \(\boldsymbol{ -\,2\,\sqrt[3]x}\)
	D. \(\boldsymbol{ -\,\frac 12 \sqrt{x^3}}\)
	E. \(\boldsymbol{-\,\frac {1} {2x\,\sqrt x}}\)

[ 5-1694 - op net sinds 10.5.98-(E)-14.11.2024 ]

Translation in E N G L I S H

The derivative of \(\large \frac {1} {\sqrt x} \) is equal to	A. \( 2\,\sqrt x\)
	B. \( -2\,\sqrt x\)
	C. \( -2\sqrt[3]x\)
	D. \( -\frac 12 \sqrt{x^3}\)
	E. \(- \frac {1} {2x\,\sqrt x} \)

Oplossing - Solution

$D \frac{1}{\sqrt x}=D\: x^{- \frac 12}=- \frac 12 x^{- \frac 32}= - \frac{1}{2x^{\frac 32}}=- \frac{1}{2 \sqrt{x^3}}=-\frac{1}{2x \sqrt x}$

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