Trigonometrik Fonksiyonların Türevleri

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By gurur on 12 Ağustos 2014 Bilgi Dünyası

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Trigonometrik ve ters trigonometrik fonksiyonların türevleri nasıl alınır? Trigonometrik Fonksiyonların türev formülleri.

TRİGONOMETRİK FONKSİYONLARIN TÜREVLERİ

$\displaystyle y=f\left( x \right)\to y'=f'\left( x \right)$

$\displaystyle Sinx\to Cosx$

$\displaystyle S\inf \left( x \right)\to f'\left( x \right)Cosf\left( x \right)$

$\displaystyle Cosx\to -Sinx$

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$\displaystyle Cosf\left( x \right)\to -f'\left( x \right)S\inf \left( x \right)$

$\displaystyle Tanx\to 1+Ta{{n}^{2}}x=\frac{1}{Co{{s}^{2}}x}=Se{{c}^{2}}x$

$\displaystyle Tanf\left( x \right)\to \frac{f'\left( x \right)}{Co{{s}^{2}}f\left( x \right)}$

$\displaystyle Cotx\to -\frac{1}{Si{{n}^{2}}x}=-\left( 1+Co{{t}^{2}}x \right)=Co{{\sec }^{2}}x$

$\displaystyle Cotf\left( x \right)\to -\frac{f'\left( x \right)}{Si{{n}^{2}}f\left( x \right)}$

$\displaystyle Secx\to Secx.Tanx$

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$\displaystyle Secf\left( x \right)\to f'\left( x \right)Secf\left( x \right).Tanf\left( x \right)$

$\displaystyle Co\sec x\to -Co\sec x.Cotx$

$\displaystyle Co\sec f\left( x \right)\to -f'\left( x \right)Co\sec f\left( x \right)Cotf\left( x \right)$

TERS TRİGONOMETRİK FONKSİYONLARIN TÜREVLERİ

$\displaystyle y=f\left( x \right)\to y'=f'\left( x \right)$

$\displaystyle ArcSinx\to \frac{1}{\sqrt{1-{{x}^{2}}}}$

$\displaystyle ArcS\inf \left( x \right)\to \frac{f'\left( x \right)}{\sqrt{1-{{f}^{2}}\left( x \right)}}$

$\displaystyle ArcCosx\to \frac{-1}{\sqrt{1-{{x}^{2}}}}$

$\displaystyle ArcCosf\left( x \right)\to \frac{-f'\left( x \right)}{\sqrt{1-{{f}^{2}}\left( x \right)}}$

$\displaystyle ArcTanx\to \frac{1}{1+{{x}^{2}}}$

$\displaystyle ArcTanf\left( x \right)\to \frac{f'\left( x \right)}{1+{{f}^{2}}x}$

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$\displaystyle ArcCotx\to \frac{-1}{1+{{x}^{2}}}$

$\displaystyle ArcCotf\left( x \right)\to \frac{-f'\left( x \right)}{1+{{f}^{2}}\left( x \right)}$

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