derivative of (d/(dx(e^x))/(1+x))

Lösung

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

\frac{e ^{x}}{1 + x}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

\frac{d ^{2}}{d x ^{2}} (1 + x) = 0

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

= \frac{e ^{x} ( 1 + x ) - 0 \cdot e ^{x}}{( 1 + x ) ^{2}}

Vereinfache

\frac{e ^{x} ( 1 + x ) - 0 \cdot e ^{x}}{( 1 + x ) ^{2}} : \frac{e ^{x}}{1 + x}

= \frac{e ^{x}}{1 + x}

\int 2 x (8 x^{2} - 20)^{2} d x

x \to 1 + lim (1 + \frac{1}{x - 1})

\int 7 x + 5 d x

d er i v a t i v e f (x) = sin (x^{5})

x \to - 2 lim (\frac{1}{( 2 + x ) ^{3}})