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Beliebt Rechnen >

(\partial)/(\partial y)((yln(y))/(x-1))

Lösung

\frac{\partial}{\partial y} (\frac{y ln ( y )}{x - 1})

Lösung

\frac{ln ( y ) + 1}{x - 1}

Schritte zur Lösung

\frac{\partial}{\partial y} (\frac{y ln ( y )}{x - 1})

Behandle

x

als Konstante

Entferne die Konstante:

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

= \frac{1}{x - 1} \frac{\partial}{\partial y} (y ln (y))

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = y, g = ln (y)

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

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

\frac{\partial}{\partial y} (ln (y)) = \frac{1}{y}

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

Vereinfache

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

= \frac{ln ( y ) + 1}{x - 1}

Beliebte Beispiele

integral of 2/(xsqrt(9+x^2))

integral of (6x+5)/((3x^2+5x)^6)

derivative f(x)=((1-4x))/(3+x)

derivative of 10^{9-x^2}

laplacetransform t^2sin(2t)