Trigonometrik Fonksiyonların Türevleri

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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)

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\displaystyle Cosx\to -Sinx

\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)}

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\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

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

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\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)

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\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)}}

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

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

\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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