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Beliebt Rechnen >

derivative e^tcos(t)

Lösung

ableitung von

e^{t} cos (t)

Lösung

e^{t} cos (t) - e^{t} sin (t)

Schritte zur Lösung

\frac{d}{d t} (e^{t} cos (t))

Wende die Produktregel an:

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

f = e^{t}, g = cos (t)

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

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

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

= e^{t} cos (t) + (- sin (t)) e^{t}

Vereinfache

= e^{t} cos (t) - e^{t} sin (t)

Graph

Beliebte Beispiele

(x-6)y^'+y=x^2-20

(x - 6) y^{^{'}} + y = x^{2} - 20

integral of x^3sqrt(16-x^2)

\int x^{3} 16 - x^{2} d x

integral of 8x-10y+2

\int 8 x - 10 y + 2 d y

integral of (ln(x)cos(x))sin(x)

\int (ln (x) cos (x)) sin (x) d x

y^{^{'}} = \frac{( 1 - 2 t )}{y}