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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{2}{y}

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

= \frac{2}{y}

Beliebte Beispiele

integral of 1/(sqrt(1-u^2))

\int \frac{1}{1 - u ^{2}} d u

derivative A/(y^9)+Be^y

d er i v a t i v e \frac{A}{y ^{9}} + B e^{y}

integral of 3/(x^2+9)

\int \frac{3}{x ^{2} + 9} d x

integral of t/1

\int \frac{t}{1} d t

integral of 4tan(4x)

\int 4 tan (4 x) d x