What is (d^3)/(dt^3)((y)(t^2)) ?

The answer to (d^3)/(dt^3)((y)(t^2)) is t^2(d^3y)/(dt^3)+6t(d^2y)/(dt^2)+6(dy)/(dt)

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

\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}

Solution steps

\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}

6 x y + 7 z - 6 y - 7 x z

p^{2} + (5 p + 3)

2 m x + 4 m y - 3 x - 6 y

4 x + 9 (2^{x}) + 18

f (8 x)

What is (d^3)/(dt^3)((y)(t^2)) ?
The answer to (d^3)/(dt^3)((y)(t^2)) is t^2(d^3y)/(dt^3)+6t(d^2y)/(dt^2)+6(dy)/(dt)