Standardderivata (elementära funktioners derivata)

f(x) = x^a, a är en konstant f'(x) = ax^(a-1)

f(x) = e^x f'(x) = e^x

f(x) = lnx f'(x) = 1/x

f(x) = g(x)^h(x) OMskrivning mha e^ln, potenslag, derivera sammansatt funktion

f(x) = sin(x) f'(x) = cos(x)

f(x) = cos(x) f'(x) = -sin(x)

f(x) = tan(x) f'(x) = 1/(cos(x)^2)

f(x) = cot(x) f'(x) = -1/(sin(x)^2)

f(x) = arcsin(x) f'(x) = 1/(√(1-x^2))

f(x) = arccos(x) f'(x) = - 1/(√(1-x^2))

f(x) = arctan(x) 1/(x^2 + 1)

f(x) = arccot(x) f'(x) = - 1/(x^2 + 1)

Produktregeln: f(x)*g'(x) + f'(x)g(x)

Kvotregeln: (f(x)g'(x) - f'(x)g(x)) / (g(x))^2

Sammansatt funktion (f(g(x)): f'(g(x)*g'(x)

Klicka