|
|
|
|
|
|
|
|
|
|
|
|
Afgeleide van $$$\operatorname{asec}{\left(x \right)}$$$
Gerelateerde rekenmachines: Rekenmachine voor logaritmisch differentiëren, Rekenmachine voor impliciete differentiatie met stappen
Uw invoer
Bepaal $$$\frac{d}{dx} \left(\operatorname{asec}{\left(x \right)}\right)$$$.
Oplossing
De afgeleide van de inverse secans is $$$\frac{d}{dx} \left(\operatorname{asec}{\left(x \right)}\right) = \frac{1}{x^{2} \sqrt{1 - \frac{1}{x^{2}}}}$$$:
$${\color{red}\left(\frac{d}{dx} \left(\operatorname{asec}{\left(x \right)}\right)\right)} = {\color{red}\left(\frac{1}{x^{2} \sqrt{1 - \frac{1}{x^{2}}}}\right)}$$Vereenvoudig:
$$\frac{1}{x^{2} \sqrt{1 - \frac{1}{x^{2}}}} = \frac{\left|{x}\right|}{x^{2} \sqrt{x^{2} - 1}}$$Dus, $$$\frac{d}{dx} \left(\operatorname{asec}{\left(x \right)}\right) = \frac{\left|{x}\right|}{x^{2} \sqrt{x^{2} - 1}}$$$.
Antwoord
$$$\frac{d}{dx} \left(\operatorname{asec}{\left(x \right)}\right) = \frac{\left|{x}\right|}{x^{2} \sqrt{x^{2} - 1}}$$$A