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Beliebt Rechnen >

derivative of e^x*cos(2x)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{x}, g = cos (2 x)

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

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

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

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

Vereinfache

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

Graph

Beliebte Beispiele

derivative of tan(xsin(x))

\frac{d}{d x} (tan (x) sin (x))

derivative 4xe^x

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(\partial)/(\partial y)(4x^2+y^2-800)

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tangent f(x)=x^3-8x^2,\at x=0

t an g e n t f (x) = x^{3} - 8 x^{2}, at x = 0

integral of sec^6(x)tan^5(x)

\int sec^{6} (x) tan^{5} (x) d x