d/(dt)((4)(7+e^{-t^2}))

Lösung

\frac{d}{d t} ((4) (7 + e^{- t^{2}}))

- 8 e^{- t^{2}} t

Schritte zur Lösung

\frac{d}{d t} ((4) (7 + e^{- t^{2}}))

Entferne die Konstante:

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

= 4 \frac{d}{d t} (7 + e^{- t^{2}})

Wende die Summen-/Differenzregel an:

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

= 4 (\frac{d}{d t} (7) + \frac{d}{d t} (e^{- t^{2}}))

\frac{d}{d t} (7) = 0

\frac{d}{d t} (e^{- t^{2}}) = - 2 e^{- t^{2}} t

= 4 (0 - 2 e^{- t^{2}} t)

Vereinfache

= - 8 e^{- t^{2}} t

e x p an d d x (x^{4} + 2 x^{3} - 7)

\frac{\partial}{\partial r} ((x) (r + 3 s - t))

e x p an d (10 x y^{3} + 12 x^{3} + 6) d x + (15 x^{2} y - 5) y d y

e x p an d \frac{4 s}{( x + 2 ) ( x - 1 )}

e x p an d e^{- 2 t} (- sin (4) 4) + cos (4 t) (e^{- 2 t} - 2 t)