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)(e^z+1/x+xe^{-y})

Lösung

\frac{\partial}{\partial x} (e^{z} + \frac{1}{x} + x e^{- y})

Lösung

- \frac{1}{x ^{2}} + e^{- y}

Schritte zur Lösung

\frac{\partial}{\partial x} (e^{z} + \frac{1}{x} + x e^{- y})

Behandle

z, y

als Konstanten

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (e^{z}) + \frac{\partial}{\partial x} (\frac{1}{x}) + \frac{\partial}{\partial x} (x e^{- y})

\frac{\partial}{\partial x} (e^{z}) = 0

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

\frac{\partial}{\partial x} (x e^{- y}) = e^{- y}

= 0 - \frac{1}{x ^{2}} + e^{- y}

Vereinfache

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

Beliebte Beispiele

(dy}{dx}=\frac{4sqrt(y)ln(x))/x ,y(e)=1

\frac{d y}{d x} = \frac{4 y ln ( x )}{x}, y (e) = 1

limit as x approaches-2 of x^3+x-1

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

derivative of 7/(x+1)

\frac{d}{d x} (\frac{7}{x + 1})

derivative of x^2ln(x/4)

\frac{d}{d x} (x^{2} ln (\frac{x}{4}))

derivative of 6x^4(x^2-7x)

\frac{d}{d x} (6 x^{4} (x^{2} - 7 x))