derivative (410t)/((t^2+5)^3)

Lösung

ableitung von

\frac{410 t}{( t ^{2} + 5 ) ^{3}}

\frac{2050 ( - t ^{2} + 1 )}{( t ^{2} + 5 ) ^{4}}

Schritte zur Lösung

\frac{d}{d t} (\frac{410 t}{( t ^{2} + 5 ) ^{3}})

Entferne die Konstante:

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

= 410 \frac{d}{d t} (\frac{t}{( t ^{2} + 5 ) ^{3}})

Wende die Quotientenregel an:

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

= 410 \cdot \frac{\frac{d t}{d t} ( t ^{2} + 5 ) ^{3} - \frac{d}{d t} ( ( t ^{2} + 5 ) ^{3} ) t}{( ( t ^{2} + 5 ) ^{3} ) ^{2}}

\frac{d t}{d t} = 1

\frac{d}{d t} ((t^{2} + 5)^{3}) = 6 t (t^{2} + 5)^{2}

= 410 \cdot \frac{1 \cdot ( t ^{2} + 5 ) ^{3} - 6 t ( t ^{2} + 5 ) ^{2} t}{( ( t ^{2} + 5 ) ^{3} ) ^{2}}

Vereinfache

410 \cdot \frac{1 \cdot ( t ^{2} + 5 ) ^{3} - 6 t ( t ^{2} + 5 ) ^{2} t}{( ( t ^{2} + 5 ) ^{3} ) ^{2}} : \frac{2050 ( - t ^{2} + 1 )}{( t ^{2} + 5 ) ^{4}}

= \frac{2050 ( - t ^{2} + 1 )}{( t ^{2} + 5 ) ^{4}}

\frac{d}{d x} (\frac{4 - 3 x - x ^{2}}{x - 2})

x \to - 1 lim (F (x))

\int lo g_{e} (2 y + 1) d y

\int - \frac{3}{5} e^{x} d x

\int 4 - 6 x - 40 x^{3} d x