derivative y= 1/2 x+1/4 xsin(2x)

Lösung

ableitung von

y = \frac{1}{2} x + \frac{1}{4} x sin (2 x)

\frac{1 + x cos ( 2 x )}{2} + \frac{1}{4} sin (2 x)

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{2} x + \frac{1}{4} x sin (2 x))

Vereinfache

\frac{1}{2} x + \frac{1}{4} x sin (2 x) : \frac{x}{2} + \frac{x sin ( 2 x )}{4}

= \frac{d}{d x} (\frac{x}{2} + \frac{x sin ( 2 x )}{4})

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (\frac{x}{2}) + \frac{d}{d x} (\frac{x sin ( 2 x )}{4})

\frac{d}{d x} (\frac{x}{2}) = \frac{1}{2}

\frac{d}{d x} (\frac{x sin ( 2 x )}{4}) = \frac{1}{4} (sin (2 x) + 2 x cos (2 x))

= \frac{1}{2} + \frac{1}{4} (sin (2 x) + 2 x cos (2 x))

Vereinfache

\frac{1}{2} + \frac{1}{4} (sin (2 x) + 2 x cos (2 x)) : \frac{1 + x cos ( 2 x )}{2} + \frac{1}{4} sin (2 x)

= \frac{1 + x cos ( 2 x )}{2} + \frac{1}{4} sin (2 x)

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