de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

(\partial)/(\partial x)(x^{-3}y^2+xy^2+5xy)

Lösung

\frac{\partial}{\partial x} (x^{- 3} y^{2} + x y^{2} + 5 x y)

Lösung

- \frac{3 y ^{2}}{x ^{4}} + y^{2} + 5 y

Schritte zur Lösung

\frac{\partial}{\partial x} (x^{- 3} y^{2} + x y^{2} + 5 x y)

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (x^{- 3} y^{2}) + \frac{\partial}{\partial x} (x y^{2}) + \frac{\partial}{\partial x} (5 x y)

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

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

\frac{\partial}{\partial x} (5 x y) = 5 y

= - \frac{3 y ^{2}}{x ^{4}} + y^{2} + 5 y

Beliebte Beispiele

integral of 1/(x-a)

\int \frac{1}{x - a} d x

inverselaplace 8/((z^2+4)^2)

in v erse l a pl a ce \frac{8}{( z ^{2} + 4 ) ^{2}}

integral of (x^2+8x)cos(x)

\int (x^{2} + 8 x) cos (x) d x

derivative of sqrt(x^4)

\frac{d}{d x} (x^{4})

derivative of (-x^2+x(-2x^2+4x-1))

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