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Math Solver

Regel

Primitiv funktion till $sin (x)$

Eftersom derivatan av

cos (x)

är -sin(x), måste -cos(x) vara en primitiv funktion till

sin (x) .

Detta gäller endast då x anges i radianer. Man kan visa denna regel genom att derivera

F (x) = - cos (x) + C .

Värdet på konstanten C spelar ingen roll eftersom derivatan av den blir 0.

F (x) = - cos (x) + C

Derivera funktion

F^{'} (x) = - D (cos (x)) + D (C)

D(a)=0

F^{'} (x) = - D (cos (x))

$D (cos (v)) = - sin (v)$

F^{'} (x) = - (- sin (x))

-(-a)=a

F^{'} (x) = sin (x)

Eftersom man får

sin (x)

när man deriverar -cos(x) måste det vara en primitiv funktion.

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