d/(dy)(xysqrt(1-(x^2)/4-(y^2)/9))

Lösung

\frac{d}{d y} (x y 1 - \frac{x ^{2}}{4} - \frac{y ^{2}}{9})

\frac{x ( 36 - 9 x ^{2} - 8 y ^{2} )}{6 36 - 9 x ^{2} - 4 y ^{2}}

Schritte zur Lösung

\frac{d}{d y} (x y 1 - \frac{x ^{2}}{4} - \frac{y ^{2}}{9})

Behandle

x

als Konstante

Entferne die Konstante:

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

= x \frac{d}{d y} (y 1 - \frac{x ^{2}}{4} - \frac{y ^{2}}{9})

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = y, g = 1 - \frac{x ^{2}}{4} - \frac{y ^{2}}{9}

= x (\frac{d y}{d y} 1 - \frac{x ^{2}}{4} - \frac{y ^{2}}{9} + \frac{d}{d y} (1 - \frac{x ^{2}}{4} - \frac{y ^{2}}{9}) y)

\frac{d y}{d y} = 1

\frac{d}{d y} (1 - \frac{x ^{2}}{4} - \frac{y ^{2}}{9}) = - \frac{2 y}{3 - 4 y ^{2} + 36 - 9 x ^{2}}

= x (1 \cdot 1 - \frac{x ^{2}}{4} - \frac{y ^{2}}{9} + (- \frac{2 y}{3 - 4 y ^{2} + 36 - 9 x ^{2}}) y)

Vereinfache

x (1 \cdot 1 - \frac{x ^{2}}{4} - \frac{y ^{2}}{9} + (- \frac{2 y}{3 - 4 y ^{2} + 36 - 9 x ^{2}}) y) : \frac{x ( 36 - 9 x ^{2} - 8 y ^{2} )}{6 36 - 9 x ^{2} - 4 y ^{2}}

= \frac{x ( 36 - 9 x ^{2} - 8 y ^{2} )}{6 36 - 9 x ^{2} - 4 y ^{2}}

x \to 0 lim (\frac{x ^{2} - 3 x}{2 x})

\int_{- \infty}^{0} 15 x e^{3 x} d x

f (x) = 3 x + 4

\frac{d}{d x} (lo g_{2} (x + 1))

(x^{4})^{^{'}}