derivative 450(1+(3t)/(29+t^2)),4

Lösung

ableitung von

450 (1 + \frac{3 t}{29 + t ^{2}}), 4

\frac{1350 ( - t ^{2} + 29 )}{( t ^{2} + 29 ) ^{2}}

Schritte zur Lösung

\frac{d}{d t} (450 (1 + \frac{3 t}{29 + t ^{2}}))

Entferne die Konstante:

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

= 450 \frac{d}{d t} (1 + \frac{3 t}{29 + t ^{2}})

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= 450 (\frac{d}{d t} (1) + \frac{d}{d t} (\frac{3 t}{29 + t ^{2}}))

\frac{d}{d t} (1) = 0

\frac{d}{d t} (\frac{3 t}{29 + t ^{2}}) = \frac{3 ( 29 - t ^{2} )}{( 29 + t ^{2} ) ^{2}}

= 450 (0 + \frac{3 ( 29 - t ^{2} )}{( 29 + t ^{2} ) ^{2}})

Vereinfache

450 (0 + \frac{3 ( 29 - t ^{2} )}{( 29 + t ^{2} ) ^{2}}) : \frac{1350 ( - t ^{2} + 29 )}{( t ^{2} + 29 ) ^{2}}

= \frac{1350 ( - t ^{2} + 29 )}{( t ^{2} + 29 ) ^{2}}

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

d er i v a t i v e y = 2 x e^{- x}

x \to \infty lim (2.5)

\int_{0}^{4} e^{- 2 x} + 4 d x

\int 1 + e^{x} d x