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

Lösung

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

\frac{x ^{2}}{y}

Schritte zur Lösung

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

Behandle

x

als Konstante

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

t an g e n t f (x) = 4 x - 3 x, (4, 10)

\frac{d}{d x} (e^{x + l n (x)})

x \to \infty lim ((- 2)^{x})

\frac{\partial}{\partial x} (2 π x y + π x^{2})

\frac{\partial}{\partial x} (e^{- 3 x})