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Beliebt Rechnen >

(\partial)/(\partial y)(ln(x^3y))

Lösung

\frac{\partial}{\partial y} (ln (x^{3} y))

Lösung

\frac{1}{y}

Schritte zur Lösung

\frac{\partial}{\partial y} (ln (x^{3} y))

Behandle

x

als Konstante

Wende die Kettenregel an:

\frac{1}{x ^{3} y} \frac{\partial}{\partial y} (x^{3} y)

= \frac{1}{x ^{3} y} \frac{\partial}{\partial y} (x^{3} y)

\frac{\partial}{\partial y} (x^{3} y) = x^{3}

= \frac{1}{x ^{3} y} x^{3}

Vereinfache

\frac{1}{x ^{3} y} x^{3} : \frac{1}{y}

= \frac{1}{y}

Beliebte Beispiele

(\partial)/(\partial h)(4/3 pir^2h)

\frac{\partial}{\partial h} (\frac{4}{3} π r^{2} h)

integral of 3/(1+4x^2)

\int \frac{3}{1 + 4 x ^{2}} d x

integral of 3x^2(2x^2-5)

\int 3 x^{2} (2 x^{2} - 5) d x

derivative of (sqrt(x)/(x^2))

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

y^{''}-2y^'+y=e^xln(x)

y^{^{''}} - 2 y^{^{'}} + y = e^{x} ln (x)