derivative of ln(x^2y^2)

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\frac{d}{d x} (3 x^{2} + 2 x^{5})

x \to \infty lim (\frac{3 x ^{2} + 10 x - 7}{2 x ^{2} - 5 x})

y^{^{''}} - 6 y^{^{'}} + 25 y = - 45 cos (2 t) + 30 sin (2 t)

\frac{d}{d x} (ln (coth (x)))

\int \frac{cos ( 5 x )}{e ^{s i n (5 x)}} d x