derivative of (z(z/(z+2)+1))

Lösung

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

\frac{x ^{2} + 4 x}{( x + 2 ) ^{2}} + 1

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x, g = \frac{x}{x + 2} + 1

= \frac{d x}{d x} (\frac{x}{x + 2} + 1) + \frac{d}{d x} (\frac{x}{x + 2} + 1) x

\frac{d x}{d x} = 1

\frac{d}{d x} (\frac{x}{x + 2} + 1) = \frac{2}{( x + 2 ) ^{2}}

= 1 \cdot (\frac{x}{x + 2} + 1) + \frac{2}{( x + 2 ) ^{2}} x

Vereinfache

1 \cdot (\frac{x}{x + 2} + 1) + \frac{2}{( x + 2 ) ^{2}} x : \frac{x ^{2} + 4 x}{( x + 2 ) ^{2}} + 1

= \frac{x ^{2} + 4 x}{( x + 2 ) ^{2}} + 1

e x p an d - \frac{l k ( l sin ( \frac{2 π x}{l} ) + 2 C π )}{4 π ^{2}}

e x p an d 3 (y - 40 = - 38)

e x p an d f (∣ x ∣ - 1) e^{∣ x ∣}

e x p an d 1 - x ((- 2 - x) (4 - x))

e x p an d \frac{[ x ( x - 1 ) - 2 ]}{2}