derivative of ln(xy^2)

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\frac{d}{d x} (\frac{1}{6 x ^{2}})

\int \frac{1}{( x ^{2} - 4 x + 4 ) ( x ^{2} - 5 x + 6 )} d x

\int - 1 sin^{3} (x) cos^{2} (x) d x

a re a x^{2} + 1, 3 - x, x = 0

\frac{d}{d x} ((\frac{tan ( x )}{x})^{2})