derivative y= x/(x+1)

Lösung

ableitung von

y = \frac{x}{x + 1}

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

1 \cdot (x + 1) - 1 \cdot x = 1

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

x \to - 9 + lim (\frac{x + 8}{x + 9})

\int \frac{1}{4 x ^{2} + 4 ^{2}} d x

k = 0 \sum \infty - 5 (\frac{3}{2})^{k + 2}

y^{^{'}} = y (x y^{5} + 3)

x \to - 3 lim (x^{3} - 2 x^{2} + x + 7)