 Matematica
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Alcuni derivati di base
- $u,v,w\text{ fonksiyonlar }, x \text{degisken}, a,b,c,n \text{ sabitler olmak üzere}$
- 1.
- $\displaystyle \frac{\displaystyle d}{\displaystyle dx}\displaystyle \left ( \displaystyle c \displaystyle \right )=\displaystyle 0$
- 2.
- $\displaystyle \frac{\displaystyle d}{\displaystyle dx}\displaystyle \left ( \displaystyle x \displaystyle \right )=\displaystyle 1$
- 3.
- $\displaystyle \frac{\displaystyle d}{\displaystyle dx}\displaystyle \left ( \displaystyle x^n \displaystyle \right )=\displaystyle nx^{\displaystyle {n-1}}$
- 4.
- $\displaystyle \frac{\displaystyle d}{\displaystyle dx}\displaystyle \left ( \displaystyle u\pm v \displaystyle \right )=\displaystyle \frac{du}{dx}\pm \displaystyle \frac{dv}{dx}$
- 5.
- $\displaystyle \frac{\displaystyle d}{\displaystyle dx}\displaystyle \left ( \displaystyle cu \displaystyle \right )=\displaystyle c\displaystyle \frac{du}{dx}$
- 6.
- $\displaystyle \frac{\displaystyle d}{\displaystyle dx}\displaystyle \left ( \displaystyle u.v \displaystyle \right )=\displaystyle u\displaystyle \frac{dv}{dx}+\displaystyle v\displaystyle \frac{du}{dx}$
- 7.
- $\displaystyle \frac{d}{dx} \left ( \displaystyle \frac{u}{v} \right )=\displaystyle \frac{v\displaystyle \frac{du}{dx}-u\displaystyle \frac{dv}{dx}}{v^2}$
- 8.
- $\displaystyle \frac{d}{dx} \left ( \displaystyle u^n \right )=\displaystyle nu^{n-1} \displaystyle\frac{du}{dx}$
- 9.
- $\displaystyle \frac{d}{dx} \left ( \displaystyle u \circ v \right )=\displaystyle\frac{dv}{dx}\left (\displaystyle\frac{du}{dx} \circ v \right )$
- 10.
- $\displaystyle \frac{du}{dx} =\displaystyle\frac{du}{dv}\displaystyle\frac{dv}{dx}$
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