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Beliebt Rechnen >

(\partial)/(\partial y)(ln(sqrt(xy)))

Lösung

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

Lösung

\frac{1}{2 y}

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Kettenregel an:

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

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

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

= \frac{1}{x y} \cdot \frac{1}{2 x y} x

Vereinfache

\frac{1}{x y} \cdot \frac{1}{2 x y} x : \frac{1}{2 y}

= \frac{1}{2 y}

Beliebte Beispiele

integral of (1/(xsqrt(x^2-1)))

\int (\frac{1}{x x ^{2} - 1}) d x

y^{''}+4y^'+5y=-5x+3e^{-x}

y^{^{''}} + 4 y^{^{'}} + 5 y = - 5 x + 3 e^{- x}

d/(dθ)(cos(θ)-2sin(θ))

\frac{d}{d θ} (cos (θ) - 2 sin (θ))

limit as x approaches 0-of ax^2+b/2

x \to 0 - lim (a x^{2} + \frac{b}{2})

tangent 2/(x^2),\at (1.2)

t an g e n t \frac{2}{x ^{2}}, at (1.2)