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Beliebt Rechnen >

derivative of ln(x^2y)

Lösung

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

Lösung

\frac{2 y + x \frac{d y}{d x}}{x y}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (x^{2} y) = 2 x y + \frac{d y}{d x} x^{2}

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

Vereinfache

\frac{1}{x ^{2} y} (2 x y + \frac{d y}{d x} x^{2}) : \frac{2 y + x \frac{d y}{d x}}{x y}

= \frac{2 y + x \frac{d y}{d x}}{x y}

Beliebte Beispiele

derivative of (6x^2+8x+8/(sqrt(x)))

derivative of 84x^6+12x^3-24x^2

integral of (1-2x)^4

integral of 1/((4+9x^2))

x^2y^{''}+3xy^'-4y=0