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Beliebt Rechnen >

(\partial)/(\partial y)(ln(x^2y^2))

Lösung

\frac{\partial}{\partial y} (ln (x^{2} y^{2}))

Lösung

\frac{2}{y}

Schritte zur Lösung

\frac{\partial}{\partial y} (ln (x^{2} y^{2}))

Behandle

x

als Konstante

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

= \frac{2}{y}

Beliebte Beispiele

integral of 3xsin^2(x)

\int 3 x sin^{2} (x) d x

integral from 0 to 1 of-1/(x-5)+2/(x-2)

\int_{0}^{1} - \frac{1}{x - 5} + \frac{2}{x - 2} d x

integral of (2x+6)^5

\int (2 x + 6)^{5} d x

derivative 3cos^3(t)

d er i v a t i v e 3 cos^{3} (t)

derivative y=e^x(3-5x+3x^2)

d er i v a t i v e y = e^{x} (3 - 5 x + 3 x^{2})