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Beliebt Rechnen >

(\partial)/(\partial y)(ln(1+xy))

Lösung

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

Lösung

\frac{x}{1 + x y}

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Kettenregel an:

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

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

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

= \frac{1}{1 + x y} x

Vereinfache

\frac{1}{1 + x y} x : \frac{x}{1 + x y}

= \frac{x}{1 + x y}

Beliebte Beispiele

sum from n=1 to infinity of 1/n-1/(2n+1)

n = 1 \sum \infty \frac{1}{n} - \frac{1}{2 n + 1}

taylor sqrt(1-x^2),0

t a y l or 1 - x^{2}, 0

derivative of sqrt(2-3x^2)

\frac{d}{d x} (2 - 3 x^{2})

derivative f(x)=(x^2)/(1+4x)

d er i v a t i v e f (x) = \frac{x ^{2}}{1 + 4 x}

integral of 1/((arcsin(x))^3sqrt(1-x^2))

\int \frac{1}{( arcsin ( x ) ) ^{3} 1 - x ^{2}} d x