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Beliebt Rechnen >

derivative of 1/2 (e^x-cos(x))

Lösung

\frac{d}{d x} (\frac{1}{2} (e^{x} - cos (x)))

Lösung

\frac{1}{2} (e^{x} + sin (x))

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{2} (e^{x} - cos (x)))

Entferne die Konstante:

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

= \frac{1}{2} \frac{d}{d x} (e^{x} - cos (x))

Wende die Summen-/Differenzregel an:

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

= \frac{1}{2} (\frac{d}{d x} (e^{x}) - \frac{d}{d x} (cos (x)))

\frac{d}{d x} (e^{x}) = e^{x}

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

= \frac{1}{2} (e^{x} - (- sin (x)))

Vereinfache

= \frac{1}{2} (e^{x} + sin (x))

Graph

Beliebte Beispiele

integral of 7xe^x

\int 7 x e^{x} d x

derivative-3cos(x)

d er i v a t i v e - 3 cos (x)

derivative f(x)=5x^2cos(x)+x

d er i v a t i v e f (x) = 5 x^{2} cos (x) + x

integral of 1/(4x+5)

\int \frac{1}{4 x + 5} d x

integral of 1 sqrt(tan(x))

\int \frac{d}{1} tan (x) d x