derivative of xy+1

Lösung

\frac{d}{d x} (x y + 1)

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

Schritte zur Lösung

\frac{d}{d x} (x y + 1)

Wende die Summen-/Differenzregel an:

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

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

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

\frac{d}{d x} (1) = 0

= y + x \frac{d y}{d x} + 0

Vereinfache

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