What is (d^2)/(dt^2)((x^2)(2sqrt(t)-1)) ?

The answer to (d^2)/(dt^2)((x^2)(2sqrt(t)-1)) is

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(d^2)/(dt^2)((x^2)(2sqrt(t)-1))

\frac{d ^{2}}{d t ^{2}} ((x^{2}) (2 t - 1))

\frac{8 t x \frac{d x}{d t} - x ^{2} + 8 t ^{2} \frac{d x}{d t} ^{2} - 4 t t \frac{d x}{d t} ^{2} + 8 t ^{2} x \frac{d ^{2} x}{d t ^{2}} - 4 t t x \frac{d ^{2} x}{d t ^{2}}}{2 t t}

Solution steps

\frac{d ^{2}}{d t ^{2}} ((x^{2}) (2 t - 1))

\frac{d}{d t} (x^{2} (2 t - 1)) = 2 x \frac{d x}{d t} (2 t - 1) + \frac{x ^{2}}{t}

= \frac{d}{d t} (2 x \frac{d x}{d t} (2 t - 1) + \frac{x ^{2}}{t})

\frac{d}{d t} (2 x \frac{d x}{d t} (2 t - 1) + \frac{x ^{2}}{t}) = \frac{8 t x \frac{d x}{d t} - x ^{2} + 8 t ^{2} \frac{d x}{d t} ^{2} - 4 t t \frac{d x}{d t} ^{2} + 8 t ^{2} x \frac{d ^{2} x}{d t ^{2}} - 4 t t x \frac{d ^{2} x}{d t ^{2}}}{2 t t}

= \frac{8 t x \frac{d x}{d t} - x ^{2} + 8 t ^{2} \frac{d x}{d t} ^{2} - 4 t t \frac{d x}{d t} ^{2} + 8 t ^{2} x \frac{d ^{2} x}{d t ^{2}} - 4 t t x \frac{d ^{2} x}{d t ^{2}}}{2 t t}

\frac{j - 1}{( j + 2 ) ( j + 4 )}

\frac{7 x + 25}{( x + 4 ) ( x + 3 )}

\frac{d}{d t} ((z (t, x, y)) (x^{2} + y^{5}))

\frac{9 x - 8}{( x - 3 ) ( 2 x - 5 )}

\frac{1}{4} (e^{2 x} + e^{- 2 x})

What is (d^2)/(dt^2)((x^2)(2sqrt(t)-1)) ?
The answer to (d^2)/(dt^2)((x^2)(2sqrt(t)-1)) is