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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{1}{y + z}

Schritte zur Lösung

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

Behandle

y, z

als Konstanten

Entferne die Konstante:

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

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

Wende die Summen-/Differenzregel an:

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

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

Vereinfache

= \frac{1}{y + z}

Beliebte Beispiele

integral of ((cos(x)))/(sin^2(x))

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

(dy)/(dx)+2x^{-1}y=6x^4y^2

\frac{d y}{d x} + 2 x^{- 1} y = 6 x^{4} y^{2}

(1/8)y^{''}+4y^'+20y=0

(\frac{1}{8}) y^{^{''}} + 4 y^{^{'}} + 20 y = 0

integral of 30(x+9)(x+9)^4

\int 30 (x + 9) (x + 9)^{4} d x

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

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