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^2}+yln(x^2+5))

Lösung

\frac{\partial}{\partial x} (e^{z^{2}} + y ln (x^{2} + 5))

Lösung

\frac{2 y x}{x ^{2} + 5}

Schritte zur Lösung

\frac{\partial}{\partial x} (e^{z^{2}} + y ln (x^{2} + 5))

Behandle

z, y

als Konstanten

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (e^{z^{2}}) + \frac{\partial}{\partial x} (y ln (x^{2} + 5))

\frac{\partial}{\partial x} (e^{z^{2}}) = 0

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

= 0 + \frac{2 y x}{x ^{2} + 5}

Vereinfache

= \frac{2 y x}{x ^{2} + 5}

Beliebte Beispiele

(dy)/(dx)= y/x+2x+3

\frac{d y}{d x} = \frac{y}{x} + 2 x + 3

(dy)/(dt)=(y+1)(y-3),y(0)=1

\frac{d y}{d t} = (y + 1) (y - 3), y (0) = 1

limit as x approaches 4/3 of 2x^2-4x+5

x \to \frac{4}{3} lim (2 x^{2} - 4 x + 5)

integral of x(3^{-x^2})

\int x (3^{- x^{2}}) d x

limit as x approaches 1 of 1.7496

x \to 1 lim (1.7496)