(\partial)/(\partial x)((ax-5)/(-y^2+1))

Lösung

\frac{\partial}{\partial x} (\frac{a x - 5}{- y ^{2} + 1})

\frac{a}{- y ^{2} + 1}

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{a x - 5}{- y ^{2} + 1})

Behandle

a, y

als Konstante

Entferne die Konstante:

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

= \frac{1}{- y ^{2} + 1} \frac{\partial}{\partial x} (a x - 5)

Wende die Summen-/Differenzregel an:

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

= \frac{1}{- y ^{2} + 1} (\frac{\partial}{\partial x} (a x) - \frac{\partial}{\partial x} (5))

\frac{\partial}{\partial x} (a x) = a

\frac{\partial}{\partial x} (5) = 0

= \frac{1}{- y ^{2} + 1} (a - 0)

Vereinfache

\frac{1}{- y ^{2} + 1} (a - 0) : \frac{a}{- y ^{2} + 1}

= \frac{a}{- y ^{2} + 1}

x \to 0 + lim (arctan (x))

\int \frac{x ^{4}}{4 + x ^{2}} d x

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