What is (d^2)/(dt^2)((y)(Ay)) ?

The answer to (d^2)/(dt^2)((y)(Ay)) is 2A((dy)/(dt)^2+(d^2y)/(dt^2)y)

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(d^2)/(dt^2)((y)(Ay))

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

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

Solution steps

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

Simplify

(y) (A y) : A y^{2}

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

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

= \frac{d}{d t} (A \cdot 2 y \frac{d y}{d t})

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

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

x^{2 + 3 x + 2}

2 (8^{3})

(p)^{2}

(2 x^{2}) + (x - 6)

\frac{d}{d x} ((d) (cos (3 x)))

What is (d^2)/(dt^2)((y)(Ay)) ?
The answer to (d^2)/(dt^2)((y)(Ay)) is 2A((dy)/(dt)^2+(d^2y)/(dt^2)y)