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Beliebt Rechnen >

(\partial)/(\partial x)(yln(x+y))

Lösung

\frac{\partial}{\partial x} (y ln (x + y))

Lösung

\frac{y}{x + y}

Schritte zur Lösung

\frac{\partial}{\partial x} (y ln (x + y))

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Wende die Kettenregel an:

\frac{1}{x + y} \frac{\partial}{\partial x} (x + y)

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

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

= y \frac{1}{x + y} \cdot 1

Vereinfache

y \frac{1}{x + y} \cdot 1 : \frac{y}{x + y}

= \frac{y}{x + y}

Beliebte Beispiele

integral of 16e^{-16x}

\int 16 e^{- 16 x} d x

(\partial)/(\partial x)(e^{(x^2)/(y^3)})

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

integral of 6x^5-4x^2+7/3

\int 6 x^{5} - 4 x^{2} + \frac{7}{3} d x

limit as t approaches 0 of f(t)

t \to 0 lim (f (t))

derivative of (2x-3/(x-1))

\frac{d}{d x} (\frac{2 x - 3}{x - 1})