Kalkulus

Her finner du formler for kalkulus. Mange synes at kalkulus er vanskelig siden man jobber mye med integraler og differensialer, så vi håper at disse formlene hjelper.

Formel for derivasjon: `f'(x) = \lim_{{h \to 0}} \frac{f(x+h) – f(x)}{h}`

Formel for den andrederiverte: `f»(x) = \lim_{{h \to 0}} \frac{f'(x+h) – f'(x)}{h}`

Formel for integral: `F(x) = \int_{a}^{x} f(t) \,dt`

Formel for partiell derivasjon: `\frac{\partial f}{\partial x} = \lim_{{h \to 0}} \frac{f(x+h, y) – f(x, y)}{h}`

Formel for gradient: `\nabla f = \left( \frac{\partial f}{\partial x}, \frac{\partial f}{\partial y} \right)`

Formel for divergens: `\nabla \cdot F = \frac{\partial F_x}{\partial x} + \frac{\partial F_y}{\partial y}`

Formel for Laplace-operatoren: `\Delta f = \nabla^2 f = \frac{\partial^2 f}{\partial x^2} + \frac{\partial^2 f}{\partial y^2}`

Formel for Taylors formel: `f(x) = f(a) + f'(a)(x-a) + \frac{f»(a)}{2!}(x-a)^2 + \frac{f»'(a)}{3!}(x-a)^3 + \cdots`

Formel for produktregelen: `(fg)’ = f’g + fg’`

Formel for kvotientregelen: `\left(\frac{f}{g}\right)’ = \frac{f’g – fg’}{g^2}`