 Matematica
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Derivati delle funzioni trigonometriche
- 1.
- $\displaystyle \frac{d}{dx}\left ( \sin u \right ) =\displaystyle \cos u \displaystyle\frac{du}{dx}$
- 2.
- $\displaystyle \frac{d}{dx}\left ( \cos u \right ) =\displaystyle -\sin u \displaystyle\frac{du}{dx}$
- 3.
- $\displaystyle \frac{d}{dx}\left ( \tan u \right ) =\displaystyle \sec^2 u \displaystyle\frac{du}{dx}$
- 4.
- $\displaystyle \frac{d}{dx}\left ( \cot u \right ) =\displaystyle -\csc^2 u \displaystyle\frac{du}{dx}$
- 5.
- $\displaystyle \frac{d}{dx}\left ( \sec u \right ) =\displaystyle \sec u \displaystyle \tan u \displaystyle\frac{du}{dx}$
- 6.
- $\displaystyle \frac{d}{dx}\left ( \csc u \right ) =\displaystyle -\csc u \displaystyle \cot u \displaystyle\frac{du}{dx}$
- 7.
- $\displaystyle \frac{d}{dx}\left ( \sin^{-1} u \right ) =\displaystyle \frac{1}{\displaystyle\sqrt{1-u^2}} \displaystyle\frac{du}{dx}$
- 8.
- $\displaystyle \frac{d}{dx}\left ( \cos^{-1} u \right ) =\displaystyle -\frac{1}{\displaystyle\sqrt{1-u^2}} \displaystyle\frac{du}{dx}$
- 9.
- $\displaystyle \frac{d}{dx}\left ( \tan^{-1} u \right ) =\displaystyle \frac{1}{\displaystyle{1+u^2}} \displaystyle\frac{du}{dx}$
- 10.
- $\displaystyle \frac{d}{dx}\left ( \cot^{-1} u \right ) =\displaystyle -\frac{1}{\displaystyle{1+u^2}} \displaystyle\frac{du}{dx}$
- 11.
- $\displaystyle \frac{d}{dx}\left ( \sec^{-1} u \right ) =\displaystyle \frac{1}{\displaystyle\left | u \right | \sqrt{1+u^2}} \displaystyle\frac{du}{dx}$
- 12.
- $\displaystyle \frac{d}{dx}\left ( \csc^{-1} u \right ) =\displaystyle -\frac{1}{\displaystyle\left | u \right | \sqrt{1+u^2}} \displaystyle\frac{du}{dx}$
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