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Beliebt Rechnen >

derivative y=(t^2+3)e^t

Lösung

ableitung von

y = (t^{2} + 3) e^{t}

Lösung

2 t e^{t} + e^{t} (t^{2} + 3)

Schritte zur Lösung

\frac{d}{d t} ((t^{2} + 3) e^{t})

Wende die Produktregel an:

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

f = t^{2} + 3, g = e^{t}

= \frac{d}{d t} (t^{2} + 3) e^{t} + \frac{d}{d t} (e^{t}) (t^{2} + 3)

\frac{d}{d t} (t^{2} + 3) = 2 t

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

= 2 t e^{t} + e^{t} (t^{2} + 3)

Graph

Beliebte Beispiele

tangent y=3+4x^2-2x^3

t an g e n t y = 3 + 4 x^{2} - 2 x^{3}

y^{''}+9y=tsin(5t)

y^{^{''}} + 9 y = t sin (5 t)

derivative of \sqrt[5]{5x-4}

\frac{d}{d x} (5 5 x - 4)

integral of 5e^{2x+e^{2x}}

\int 5 e^{2 x + e^{2 x}} d x

integral of sqrt(x^2+y^2)

\int x^{2} + y^{2} d x