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Beliebt Rechnen >

derivative of-2(e^xsin(x+cos(x)e^x))

Lösung

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

Lösung

- 4 e^{x} cos (x)

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Summen-/Differenzregel an:

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

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

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

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

= - 2 (e^{x} sin (x) + cos (x) e^{x} - e^{x} sin (x) + e^{x} cos (x))

Vereinfache

= - 4 e^{x} cos (x)

Graph

Beliebte Beispiele

integral of 1/(5+2x^4)(8x^3)

\int \frac{1}{5 + 2 x ^{4}} (8 x^{3}) d x

derivative of 8sin(x-4sqrt(2x))

\frac{d}{d x} (8 sin (x) - 4 2 x)

derivative of 1/(\sqrt[5]{x^2})

\frac{d}{d x} (\frac{1}{5 x ^{2}})

laplacetransform {cos(t)}

l a pl a ce t r an s f or m {cos (t)}

f (t) = cos (8 t)