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Beliebt Rechnen >

(\partial)/(\partial y)(x*ln(y-z))

Lösung

\frac{\partial}{\partial y} (x \cdot ln (y - z))

Lösung

\frac{x}{y - z}

Schritte zur Lösung

\frac{\partial}{\partial y} (x ln (y - z))

Behandle

x, z

als Konstanten

Entferne die Konstante:

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

= x \frac{\partial}{\partial y} (ln (y - z))

Wende die Kettenregel an:

\frac{1}{y - z} \frac{\partial}{\partial y} (y - z)

= \frac{1}{y - z} \frac{\partial}{\partial y} (y - z)

\frac{\partial}{\partial y} (y - z) = 1

= x \frac{1}{y - z} \cdot 1

Vereinfache

x \frac{1}{y - z} \cdot 1 : \frac{x}{y - z}

= \frac{x}{y - z}

Beliebte Beispiele

integral of (x^3)/(x^4+3x^2+2)

\int \frac{x ^{3}}{x ^{4} + 3 x ^{2} + 2} d x

integral from 1 to 7 of 1/(36+(x+5)^2)

\int_{1}^{7} \frac{1}{36 + ( x + 5 ) ^{2}} d x

derivative of (x^2-4/(x^2+4))

\frac{d}{d x} (\frac{x ^{2} - 4}{x ^{2} + 4})

integral of (-2x^4-4x^2-5)

\int (- 2 x^{4} - 4 x^{2} - 5) d x

integral of 2cos(x/2)

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