derivative of (sin(x)/(e^x))

Lösung

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

\frac{cos ( x ) - sin ( x )}{e ^{x}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( sin ( x ) ) e ^{x} - \frac{d}{d x} ( e ^{x} ) sin ( x )}{( e ^{x} ) ^{2}}

\frac{d}{d x} (sin (x)) = cos (x)

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

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

Vereinfache

\frac{cos ( x ) e ^{x} - e ^{x} sin ( x )}{( e ^{x} ) ^{2}} : \frac{cos ( x ) - sin ( x )}{e ^{x}}

= \frac{cos ( x ) - sin ( x )}{e ^{x}}

\int \frac{x}{2 x - 3} d x

\frac{\partial}{\partial x} (2 x y^{3} - 1)

\frac{d y}{d t} = \frac{t}{y + 1}

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

d er i v a t i v e f (x) = - x + \frac{4}{x} + 1