(d^3)/(dt^3)((y)(t^2))

Lösung

\frac{d ^{3}}{d t ^{3}} ((y) (t^{2}))

t^{2} \frac{d ^{3} y}{d t ^{3}} + 6 t \frac{d ^{2} y}{d t ^{2}} + 6 \frac{d y}{d t}

Schritte zur Lösung

\frac{d ^{3}}{d t ^{3}} ((y) (t^{2}))

\frac{d}{d t} (y t^{2}) = \frac{d y}{d t} t^{2} + 2 t y

= \frac{d ^{2}}{d t ^{2}} (\frac{d y}{d t} t^{2} + 2 t y)

\frac{d}{d t} (\frac{d y}{d t} t^{2} + 2 t y) = t^{2} \frac{d ^{2} y}{d t ^{2}} + 4 t \frac{d y}{d t} + 2 y

= \frac{d}{d t} (t^{2} \frac{d ^{2} y}{d t ^{2}} + 4 t \frac{d y}{d t} + 2 y)

\frac{d}{d t} (t^{2} \frac{d ^{2} y}{d t ^{2}} + 4 t \frac{d y}{d t} + 2 y) = t^{2} \frac{d ^{3} y}{d t ^{3}} + 6 t \frac{d ^{2} y}{d t ^{2}} + 6 \frac{d y}{d t}

= t^{2} \frac{d ^{3} y}{d t ^{3}} + 6 t \frac{d ^{2} y}{d t ^{2}} + 6 \frac{d y}{d t}

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