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Beliebt Rechnen >

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

Lösung

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

Lösung

- \frac{1}{2 x}

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

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

\frac{\partial}{\partial x} (y) = 0

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

= 0 - \frac{1}{2 x}

Vereinfache

= - \frac{1}{2 x}

Beliebte Beispiele

(d^2)/(dx^2)((14t^2+6)^{0.5})

\frac{d ^{2}}{d x ^{2}} ((14 t^{2} + 6)^{0.5})

10x^{''}+1000x=0

10 x^{^{''}} + 1000 x = 0

derivative of (4pix^3/3)

\frac{d}{d x} (\frac{4 π x ^{3}}{3})

(e^{x} + e^{- x})^{^{'}}

x(x+1)y^'+xy=1,y(e)=1

x (x + 1) y^{^{'}} + x y = 1, y (e) = 1