 Matematica
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Derivati delle funzioni esponenziali e logaritmiche
- 1.
- $\displaystyle \frac{d}{dx}\left ( \ln u \right ) =\displaystyle \frac{1}{u} \displaystyle\frac{du}{dx}$
- 2.
- $\displaystyle \frac{d}{dx}\left ( \log_a u \right ) =\displaystyle \frac{1}{u\ln a} \displaystyle\frac{du}{dx}$
- 3.
- $\displaystyle \frac{d}{dx}\left ( e^{\displaystyle u} \right ) =\displaystyle e^{\displaystyle u} \displaystyle\frac{du}{dx}$
- 4.
- $\displaystyle \frac{d}{dx}\left ( a^{\displaystyle u} \right ) =\displaystyle a^{\displaystyle u} \displaystyle \ln a\displaystyle\frac{du}{dx}$
- 5.
- $\displaystyle \frac{d}{dx}\left ( u^{\displaystyle v} \right )=\displaystyle \frac{d}{dx}\left ( e^{\displaystyle v\ln u} \right ) = e^{\displaystyle v\ln u} \displaystyle \left( v \ln u\displaystyle \right) \frac{du}{dx}$
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