derivative of arctan(e^xx^2)

Lösung

\frac{d}{d x} (arctan (e^{x} x^{2}))

\frac{e ^{x} x ^{2} + 2 e ^{x} x}{e ^{2 x} x ^{4} + 1}

Schritte zur Lösung

\frac{d}{d x} (arctan (e^{x} x^{2}))

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

= \frac{e ^{x} x ^{2} + 2 e ^{x} x}{e ^{2 x} x ^{4} + 1}

x \to 0 lim (\frac{4}{x})

t y^{^{'}} - 4 y = t^{6} e^{t}

d er i v a t i v e \frac{11}{( 9 x + 11 ) ^{2}}

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

\frac{d}{d x} (x e^{4 x} + cos (2 x))