de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

derivative of (e^x+1/(x^2))

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

derivative of 6x^4-2x^3-12x^2+3x+3

\frac{d}{d x} (6 x^{4} - 2 x^{3} - 12 x^{2} + 3 x + 3)

(d^2)/(dx^2)(4/(5t^6))

\frac{d ^{2}}{d x ^{2}} (\frac{4}{5 t ^{6}})

derivative e^{2-x}

d er i v a t i v e e^{2 - x}

y^{^{'}} = 23 x y

integral of (tan(2x)-sec(2x))

\int (tan (2 x) - sec (2 x)) d x