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Beliebt Rechnen >

derivative of xy+y-1

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (x y) + \frac{d y}{d x} - \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} + \frac{d y}{d x} - 0

Vereinfache

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

Beliebte Beispiele

integral from 4 to 5 of 1/((x-4)^{4/3)}

\int_{4}^{5} \frac{1}{( x - 4 ) ^{\frac{4}{3}}} d x

derivative f(x)=e^{x+2}+1

d er i v a t i v e f (x) = e^{x + 2} + 1

derivative of (x^2-2/(x-1))

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

limit as x approaches 0 of ln|x|

x \to 0 lim (ln ∣ x ∣)

derivative of (x+3/2)

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