(d^2)/(dt^2)((x)(t^3-15t^2+54t))

Lösung

\frac{d ^{2}}{d t ^{2}} ((x) (t^{3} - 15 t^{2} + 54 t))

\frac{d ^{2} x}{d t ^{2}} (t^{3} - 15 t^{2} + 54 t) + 2 \frac{d x}{d t} (3 t^{2} - 30 t + 54) + (6 t - 30) x

Schritte zur Lösung

\frac{d ^{2}}{d t ^{2}} ((x) (t^{3} - 15 t^{2} + 54 t))

\frac{d}{d t} (x (t^{3} - 15 t^{2} + 54 t)) = \frac{d x}{d t} (t^{3} - 15 t^{2} + 54 t) + (3 t^{2} - 30 t + 54) x

= \frac{d}{d t} (\frac{d x}{d t} (t^{3} - 15 t^{2} + 54 t) + (3 t^{2} - 30 t + 54) x)

\frac{d}{d t} (\frac{d x}{d t} (t^{3} - 15 t^{2} + 54 t) + (3 t^{2} - 30 t + 54) x) = \frac{d ^{2} x}{d t ^{2}} (t^{3} - 15 t^{2} + 54 t) + 2 \frac{d x}{d t} (3 t^{2} - 30 t + 54) + (6 t - 30) x

= \frac{d ^{2} x}{d t ^{2}} (t^{3} - 15 t^{2} + 54 t) + 2 \frac{d x}{d t} (3 t^{2} - 30 t + 54) + (6 t - 30) x

e x p an d sin (t) U (t - \frac{3 π}{2})

e x p an d \frac{x - 7}{( x + 6 ) ( x - 6 )}

e x p an d r (2 r^{2} - a r + a^{2})^{2}

e x p an d ln x^{2} \frac{x - 2}{x + 3}

e x p an d (8 + 2 x)^{\frac{- 1}{3}}