Hiperbolik Fonksiyonların Türevi

Bu sayfa, hiperbolik fonksiyonların türev formüllerini sunar. sinh, cosh ve tanh gibi fonksiyonların türevleri temel kurallar kullanılarak elde edilir.

1.: \(\small \displaystyle \frac{d}{dx}\left (\displaystyle \sinh u \right )=\displaystyle \cosh u \displaystyle \frac{du}{dx}\)

2.: \(\small \displaystyle \frac{d}{dx}\left (\displaystyle \cosh u \right )=\displaystyle \sinh u \displaystyle \frac{du}{dx}\)

3.: \(\small \displaystyle \frac{d}{dx}\left (\displaystyle \tanh u \right )=\displaystyle \text{sech}^2 u \displaystyle \frac{du}{dx}\)

4.: \(\small \displaystyle \frac{d}{dx}\left (\displaystyle \coth u \right )=\displaystyle -\text{csch}^2 u \displaystyle \frac{du}{dx}\)

5.: \(\small \displaystyle \frac{d}{dx}\left (\displaystyle \sinh^{-1} u \right )=\displaystyle \frac{1}{\displaystyle \sqrt{u^2+1}}\displaystyle \frac{du}{dx}\)

6.: \(\small \displaystyle \frac{d}{dx}\left (\displaystyle \cosh^{-1} u \right )=\displaystyle \frac{\pm 1}{\displaystyle \sqrt{u^2-1}}\displaystyle \frac{du}{dx}\)

7.: \(\small \displaystyle \frac{d}{dx}\left (\displaystyle \tanh^{-1} u \right )=\displaystyle \frac{\pm 1}{\displaystyle 1-u^2}\displaystyle \frac{du}{dx}\)