d/(dt)((x)(5.8t+9.7t^2))

Lösung

\frac{d}{d t} ((x) (5.8 t + 9.7 t^{2}))

\frac{d x}{d t} (5.8 t + 9.7 t^{2}) + (5.8 + 19.4 t) x

Schritte zur Lösung

\frac{d}{d t} ((x) (5.8 t + 9.7 t^{2}))

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = 5.8 t + 9.7 t^{2}

= \frac{d x}{d t} (5.8 t + 9.7 t^{2}) + \frac{d}{d t} (5.8 t + 9.7 t^{2}) x

\frac{d}{d t} (5.8 t + 9.7 t^{2}) = 5.8 + 19.4 t

= \frac{d x}{d t} (5.8 t + 9.7 t^{2}) + (5.8 + 19.4 t) x

e x p an d \frac{5 x - 105}{7 ( x + 3 )}

e x p an d \frac{( - 420 t ^{2} - 2 t + 2940 )}{( t ^{2} + 7 ) ^{2}}

\frac{d}{d θ} ((x (θ)) (2 (1 - cos (θ))))

e x p an d x^{- \frac{1}{2}} + x^{- \frac{1}{2}}

e x p an d 2 + U (t - \frac{7}{2}) e^{- t} sin (π t)