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Beliebt Rechnen >

(\partial)/(\partial x)((x+y)/(y+1))

Lösung

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

Lösung

\frac{1}{y + 1}

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Wende die Summen-/Differenzregel an:

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

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

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

\frac{\partial}{\partial x} (y) = 0

= \frac{1}{y + 1} (1 + 0)

Vereinfache

= \frac{1}{y + 1}

Beliebte Beispiele

integral of (x^2)/(x^6+3x^3+2)

\int \frac{x ^{2}}{x ^{6} + 3 x ^{3} + 2} d x

fläche x^2+1,3-x

a re a x^{2} + 1, 3 - x

derivative of 2x^{5/3}-5x^{4/5}+7x^{3/2}-8x+17

\frac{d}{d x} (2 x^{\frac{5}{3}} - 5 x^{\frac{4}{5}} + 7 x^{\frac{3}{2}} - 8 x + 17)

integral of arcsin^2(x)

\int arcsin^{2} (x) d x

derivative f(x)=(x^2)/(x-11)

d er i v a t i v e f (x) = \frac{x ^{2}}{x - 11}