de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

(\partial)/(\partial y)((xy^2)/(x^2y^3+1))

Lösung

\frac{\partial}{\partial y} (\frac{x y ^{2}}{x ^{2} y ^{3} + 1})

Lösung

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

Schritte zur Lösung

\frac{\partial}{\partial y} (\frac{x y ^{2}}{x ^{2} y ^{3} + 1})

Behandle

x

als Konstante

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= x \frac{\partial}{\partial y} (\frac{y ^{2}}{x ^{2} y ^{3} + 1})

Wende die Quotientenregel an:

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

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

\frac{\partial}{\partial y} (y^{2}) = 2 y

\frac{\partial}{\partial y} (x^{2} y^{3} + 1) = 3 x^{2} y^{2}

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

Vereinfache

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

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

Beliebte Beispiele

limit as x approaches 1 of (x+3)/(x-2)

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

fläche 6,0,16-2x

a re a 6, 0, 16 - 2 x

(dy}{dx}=\frac{xy)/3

\frac{d y}{d x} = \frac{x y}{3}

derivative of x^{-2}*ln(x)

\frac{d}{d x} (x^{- 2} \cdot ln (x))

integral from 0 to 1 of t^2e^t

\int_{0}^{1} t^{2} e^{t} d t