(\partial)/(\partial t)(e^{-t}sin(t))

Lösung

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

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

Vereinfache

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

\int (a^{5 x} + e^{5 x}) d x

\int \frac{1}{4 - y ^{2}} d y

\int sin^{8} (3 x) cos^{5} (3 x) d x

d er i v a t i v e f (x) = ln (x^{2} - 8 x + 16)

\frac{\partial}{\partial x} (cos^{2} (θ))