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)(z^{xy^2})

Lösung

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

Lösung

y^{2} z^{x y^{2}} ln (z)

Schritte zur Lösung

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

Behandle

z, y

als Konstanten

Wende Exponentenregel an:

a^{b} = e^{b l n (a)}

z^{x y^{2}} = e^{x y^{2} l n (z)}

= \frac{\partial}{\partial x} (e^{x y^{2} l n (z)})

Wende die Kettenregel an:

e^{x y^{2} l n (z)} \frac{\partial}{\partial x} (x y^{2} ln (z))

= e^{x y^{2} l n (z)} \frac{\partial}{\partial x} (x y^{2} ln (z))

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

= e^{x y^{2} l n (z)} y^{2} ln (z)

e^{x y^{2} l n (z)} = z^{x y^{2}}

= y^{2} z^{x y^{2}} ln (z)

Beliebte Beispiele

limit as x approaches 0+of (x-|x|)/(|x|)

x \to 0 + lim (\frac{x - ∣ x ∣}{∣ x ∣})

(dy)/(dt)=2te^{-y},y(0)=-2

\frac{d y}{d t} = 2 t e^{- y}, y (0) = - 2

y^{''}=4y,y(0)=0,y^'(0)=1

y^{^{''}} = 4 y, y (0) = 0, y^{^{'}} (0) = 1

y^{^{'}} = x (x - 1)

(y+x^3+xy^2)dx-xdy=0

(y + x^{3} + x y^{2}) d x - x d y = 0