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Beliebt Rechnen >

(\partial)/(\partial t)(e^tsin(t))

Lösung

\frac{\partial}{\partial t} (e^{t} sin (t))

Lösung

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

Schritte zur Lösung

\frac{\partial}{\partial t} (e^{t} sin (t))

Wende die Produktregel an:

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

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

= \frac{\partial}{\partial t} (e^{t}) sin (t) + \frac{\partial}{\partial t} (sin (t)) e^{t}

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

\frac{\partial}{\partial t} (sin (t)) = cos (t)

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

Beliebte Beispiele

derivative of 3ln(4x)

\frac{d}{d x} (3 ln (4 x))

integral from 1 to 3 of (4x-3)^2-(x^2)^2

\int_{1}^{3} (4 x - 3)^{2} - (x^{2})^{2} d x

integral of (6x^2+8)/(x^3+4x)

\int \frac{6 x ^{2} + 8}{x ^{3} + 4 x} d x

(dy)/(dx)+y=e^{7x}

\frac{d y}{d x} + y = e^{7 x}

y^'-5/x y=(y^5)/(x^{18)}

y^{^{'}} - \frac{5}{x} y = \frac{y ^{5}}{x ^{18}}