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

Lösung

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

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

Schritte zur Lösung

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

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

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

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

Vereinfache

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

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

x \to 5 - lim (8 - x - x^{2})

y^{^{'}} = \frac{x - 2}{y - 2}

\frac{\partial}{\partial x} (2 x^{2} + 3 y^{2} + 5 z^{2})

s l o p e y = (\frac{( x + 2 )}{( x - 2 ) ^{2}}), at x = 3

\frac{d}{d x} (\frac{x ^{2} - 3}{e ^{x}})