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Beliebt Rechnen >

derivative of 8(e^xcos(x-e^xsin(x)))

Lösung

\frac{d}{d x} (8 (e^{x} cos (x) - e^{x} sin (x)))

Lösung

- 16 e^{x} sin (x)

Schritte zur Lösung

\frac{d}{d x} (8 (e^{x} cos (x) - e^{x} sin (x)))

Entferne die Konstante:

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

= 8 \frac{d}{d x} (e^{x} cos (x) - e^{x} sin (x))

Wende die Summen-/Differenzregel an:

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

= 8 (\frac{d}{d x} (e^{x} cos (x)) - \frac{d}{d x} (e^{x} sin (x)))

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

\frac{d}{d x} (e^{x} sin (x)) = e^{x} sin (x) + cos (x) e^{x}

= 8 (e^{x} cos (x) - e^{x} sin (x) - (e^{x} sin (x) + cos (x) e^{x}))

Vereinfache

8 (e^{x} cos (x) - e^{x} sin (x) - (e^{x} sin (x) + cos (x) e^{x})) : - 16 e^{x} sin (x)

= - 16 e^{x} sin (x)

Graph

Beliebte Beispiele

integral of (x^4-5x^3+5x^2+8)/(x^3+3x^2)

\int \frac{x ^{4} - 5 x ^{3} + 5 x ^{2} + 8}{x ^{3} + 3 x ^{2}} d x

derivative f(x)=5x^2(x^3+2)

d er i v a t i v e f (x) = 5 x^{2} (x^{3} + 2)

derivative of 3x^{3x}

\frac{d}{d x} (3 x^{3 x})

derivative of 5-2sin(x-e^x)

\frac{d}{d x} (5 - 2 sin (x) - e^{x})

integral of t/((3t^2+1)^4)

\int \frac{t}{( 3 t ^{2} + 1 ) ^{4}} d t