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Beliebt Rechnen >

(\partial)/(\partial x)(1/(2x+y))

Lösung

\frac{\partial}{\partial x} (\frac{1}{2 x + y})

Lösung

- \frac{2}{( 2 x + y ) ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{1}{2 x + y})

Behandle

y

als Konstante

Wende Exponentenregel an:

\frac{1}{a} = a^{- 1}

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

Wende die Kettenregel an:

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

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

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

= - \frac{1}{( 2 x + y ) ^{2}} \cdot 2

Vereinfache

- \frac{1}{( 2 x + y ) ^{2}} \cdot 2 : - \frac{2}{( 2 x + y ) ^{2}}

= - \frac{2}{( 2 x + y ) ^{2}}

Beliebte Beispiele

limit as x approaches 5 of (x-5)/(x^2-5)

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

integral of (tan^4(x))/(cos^2(x))

\int \frac{tan ^{4} ( x )}{cos ^{2} ( x )} d x

(dy)/(dx)=ye^x,y(0)=2e

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

derivative of sin(yx)

\frac{d}{d x} (sin (y x))

\frac{d}{d t} (1 + t^{2})