(\partial)/(\partial x)((x^2+4)/(y-3))

Lösung

\frac{\partial}{\partial x} (\frac{x ^{2} + 4}{y - 3})

\frac{2 x}{y - 3}

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{x ^{2} + 4}{y - 3})

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{\partial}{\partial x} (4) = 0

= \frac{1}{y - 3} (2 x + 0)

Vereinfache

\frac{1}{y - 3} (2 x + 0) : \frac{2 x}{y - 3}

= \frac{2 x}{y - 3}

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

a re a x + 2, x^{2}, - 1, 2

d er i v a t i v e y = \frac{x}{3 + x}

\int - \frac{3}{x ^{3}} d x

\frac{d}{d x} (arcsin (x^{2} - 3))