derivative f(x)= x/((1+x^2))

Lösung

ableitung von

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

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

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

2 y d x - x d y = 0

d er i v a t i v e x^{2} - 6 x + 10

x \to 1 lim (x + 3)

d er i v a t i v e y = x e^{s i n (x)}

\frac{\partial}{\partial x} (x^{3} + x^{2} y^{2} + y^{3})