derivative of (10x/((x^2+1)^2))

Lösung

\frac{d}{d x} (\frac{10 x}{( x ^{2} + 1 ) ^{2}})

\frac{10 ( - 3 x ^{2} + 1 )}{( x ^{2} + 1 ) ^{3}}

Schritte zur Lösung

\frac{d}{d x} (\frac{10 x}{( x ^{2} + 1 ) ^{2}})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 10 \frac{d}{d x} (\frac{x}{( x ^{2} + 1 ) ^{2}})

Wende die Quotientenregel an:

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

= 10 \cdot \frac{\frac{d x}{d x} ( x ^{2} + 1 ) ^{2} - \frac{d}{d x} ( ( x ^{2} + 1 ) ^{2} ) x}{( ( x ^{2} + 1 ) ^{2} ) ^{2}}

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

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

= 10 \cdot \frac{1 \cdot ( x ^{2} + 1 ) ^{2} - 4 x ( x ^{2} + 1 ) x}{( ( x ^{2} + 1 ) ^{2} ) ^{2}}

Vereinfache

10 \cdot \frac{1 \cdot ( x ^{2} + 1 ) ^{2} - 4 x ( x ^{2} + 1 ) x}{( ( x ^{2} + 1 ) ^{2} ) ^{2}} : \frac{10 ( - 3 x ^{2} + 1 )}{( x ^{2} + 1 ) ^{3}}

= \frac{10 ( - 3 x ^{2} + 1 )}{( x ^{2} + 1 ) ^{3}}

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

x \to 5 lim (9 - x^{2})

\int \frac{y}{y + 3} d y

x \to 0 lim (\frac{5 x ^{2}}{x ^{4}})

\int_{0}^{2} x^{3} 3 x + 1 d x