derivative of (e^x/(x^4+1))

Lösung

\frac{d}{d x} (\frac{e ^{x}}{x ^{4} + 1})

\frac{e ^{x} ( x ^{4} + 1 ) - 4 x ^{3} e ^{x}}{( x ^{4} + 1 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{e ^{x}}{x ^{4} + 1})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( e ^{x} ) ( x ^{4} + 1 ) - \frac{d}{d x} ( x ^{4} + 1 ) e ^{x}}{( x ^{4} + 1 ) ^{2}}

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

\frac{d}{d x} (x^{4} + 1) = 4 x^{3}

= \frac{e ^{x} ( x ^{4} + 1 ) - 4 x ^{3} e ^{x}}{( x ^{4} + 1 ) ^{2}}

\frac{d}{d x} (x^{6} - 1)

\int \frac{1}{x 4 x + 49} d x

(2 y^{2} + 2 y + 4 x^{2}) d x + (2 y x + x) d y = 0

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

\int 3 sin^{4} (x co) s^{2} x d x