Analyse/Differentiatie: verschil tussen versies
Verwijderde inhoud Toegevoegde inhoud
k + {{GFDL-oud}} |
|||
Regel 116:
& = \lim_{\Delta x \to 0}\frac{\sin(x)\cos(\Delta x) + \cos(x)\sin{\Delta x} - \sin(x)}{\Delta x} \\
& = \lim_{\Delta x \to 0}\frac{\sin(x)\cos(\Delta x) - \sin(x)}{\Delta x} + \lim_{\Delta x \to 0}\frac{\cos(x)\sin(\Delta x)}{\Delta x} \\
& = \sin(x)\lim_{\Delta x \to 0}\frac{cos(\Delta x)-1}{\Delta x} + \cos(x)\lim_{\Delta x \to 0}\frac{\sin(\Delta x)}{\Delta x} \\
& = \sin(x)\lim_{\Delta x \to 0}\frac{\Big(\cos(x)-1\Big)\Big(\cos(x)+1\Big)}{\Delta x \Big(\cos(x)+1\Big)} + \cos(x)\lim_{\Delta x \to 0}\frac{\sin(\Delta x)}{\Delta x} \\
& = \sin(x)\lim_{\Delta x \to 0}\frac{\Big(\cos^2(x)-1\Big)}{\Delta x\Big(\cos(x)+1\Big)} + \cos(x)\lim_{\Delta x \to 0}\frac{\sin(\Delta x)}{\Delta x} \\
| |||