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Math Solver

Regel

Primitiv funktion till $cos (k x)$

En primitiv funktion till

cos (k x),

där k≠0, kommer alltid vara på formen

\frac{s i n ( k x )}{k} + C,

där C är en konstant.

$D^{- 1} (cos (k x)) = \frac{sin ( k x )}{k} + C$

Regeln gäller endast då x anges i radianer. Man kan motivera att detta är en primitiv funktion genom att derivera högerledet.

F (x) = \frac{sin ( k x )}{k} + C

$\frac{a}{b} = \frac{1}{b} \cdot a$

F (x) = \frac{1}{k} \cdot sin (k x) + C

Derivera funktion

F^{'} (x) = D (\frac{1}{k} \cdot sin (k x)) + D (C)

D(a)=0

F^{'} (x) = D (\frac{1}{k} \cdot sin (k x))

DeriveSinAmpFreq

$D (a sin (k v)) = a \cdot k cos (k v)$

F^{'} (x) = \frac{1}{k} \cdot k \cdot cos (k x)

FracMultDenomToNumber

$\frac{a}{k} \cdot k = a$

F^{'} (x) = cos (k x)

Derivatan blir

cos (k x),

så

\frac{s i n ( k x )}{k} + C

är de primitiva funktionerna till

cos (k x) .

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