 Matematica
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Derivati delle funzioni iperboliche
- 1.
- $\displaystyle \frac{d}{dx}\left (\displaystyle \sinh u \right )=\displaystyle \cosh u \displaystyle \frac{du}{dx}$
- 2.
- $\displaystyle \frac{d}{dx}\left (\displaystyle \cosh u \right )=\displaystyle \sinh u \displaystyle \frac{du}{dx}$
- 3.
- $\displaystyle \frac{d}{dx}\left (\displaystyle \tanh u \right )=\displaystyle \text{sech}^2 u \displaystyle \frac{du}{dx}$
- 4.
- $\displaystyle \frac{d}{dx}\left (\displaystyle \coth u \right )=\displaystyle -\text{csch}^2 u \displaystyle \frac{du}{dx}$
- 5.
- $\displaystyle \frac{d}{dx}\left (\displaystyle \sinh^{-1} u \right )=\displaystyle \frac{1}{\displaystyle \sqrt{u^2+1}}\displaystyle \frac{du}{dx}$
- 6.
- $\displaystyle \frac{d}{dx}\left (\displaystyle \cosh^{-1} u \right )=\displaystyle \frac{\pm 1}{\displaystyle \sqrt{u^2-1}}\displaystyle \frac{du}{dx}$
- 7.
- $\displaystyle \frac{d}{dx}\left (\displaystyle \tanh^{-1} u \right )=\displaystyle \frac{\pm 1}{\displaystyle 1-u^2}\displaystyle \frac{du}{dx}$
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