derivative of 1/2 (sin(x+xcos(x)))

Lösung

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

\frac{2 cos ( x ) - x sin ( x )}{2}

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Summen-/Differenzregel an:

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

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

\frac{d}{d x} (sin (x)) = cos (x)

\frac{d}{d x} (x cos (x)) = cos (x) - x sin (x)

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

Vereinfache

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

= \frac{2 cos ( x ) - x sin ( x )}{2}

x \to 5 lim (e^{6})

n = 0 \sum \infty \frac{1}{( 2 n + 1 ) ^{2}}

\frac{d}{d x} (7 - x^{2})

x \to π lim (- 6 sin (x) + 4 x)

t (\frac{d y}{d t}) + 27 y = \frac{1}{t}