What is (d^2)/(dt^2)((x(t,y(x,t)))(4y(x,t)+e^t)) ?

The answer to (d^2)/(dt^2)((x(t,y(x,t)))(4y(x,t)+e^t)) is

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(d^2)/(dt^2)((x(t,y(x,t)))(4y(x,t)+e^t))

\frac{d ^{2}}{d t ^{2}} ((x (t, y (x, t))) (4 y (x, t) + e^{t}))

x (((, (1 \frac{d}{d t} (y (x, t)) + (\frac{d ^{2}}{d t ^{2}} (y (x, t)) t + 1 \frac{d}{d t} (y (x, t))))) (4 y (x, t) + e^{t}) + (4 \frac{d}{d t} (y (x, t)) + e^{t}) (, (1 \cdot y (x, t) + \frac{d}{d t} (y (x, t)) t))) + ((4 \frac{d ^{2}}{d t ^{2}} (y (x, t)) + e^{t}) (t, y (x, t)) + (, (1 \cdot y (x, t) + \frac{d}{d t} (y (x, t)) t)) (4 \frac{d}{d t} (y (x, t)) + e^{t})))

Solution steps

\frac{d ^{2}}{d t ^{2}} ((x (t, y (x, t))) (4 y (x, t) + e^{t}))

\frac{d}{d t} (x (t, y (x, t)) (4 y (x, t) + e^{t})) = x ((, (1 \cdot y (x, t) + \frac{d}{d t} (y (x, t)) t)) (4 y (x, t) + e^{t}) + (4 \frac{d}{d t} (y (x, t)) + e^{t}) (t, y (x, t)))

= \frac{d}{d t} (x ((, (1 \cdot y (x, t) + \frac{d}{d t} (y (x, t)) t)) (4 y (x, t) + e^{t}) + (4 \frac{d}{d t} (y (x, t)) + e^{t}) (t, y (x, t))))

\frac{d}{d t} (x ((, (1 \cdot y (x, t) + \frac{d}{d t} (y (x, t)) t)) (4 y (x, t) + e^{t}) + (4 \frac{d}{d t} (y (x, t)) + e^{t}) (t, y (x, t)))) = x (((, (1 \frac{d}{d t} (y (x, t)) + (\frac{d ^{2}}{d t ^{2}} (y (x, t)) t + 1 \frac{d}{d t} (y (x, t))))) (4 y (x, t) + e^{t}) + (4 \frac{d}{d t} (y (x, t)) + e^{t}) (, (1 \cdot y (x, t) + \frac{d}{d t} (y (x, t)) t))) + ((4 \frac{d ^{2}}{d t ^{2}} (y (x, t)) + e^{t}) (t, y (x, t)) + (, (1 \cdot y (x, t) + \frac{d}{d t} (y (x, t)) t)) (4 \frac{d}{d t} (y (x, t)) + e^{t})))

= x (((, (1 \frac{d}{d t} (y (x, t)) + (\frac{d ^{2}}{d t ^{2}} (y (x, t)) t + 1 \frac{d}{d t} (y (x, t))))) (4 y (x, t) + e^{t}) + (4 \frac{d}{d t} (y (x, t)) + e^{t}) (, (1 \cdot y (x, t) + \frac{d}{d t} (y (x, t)) t))) + ((4 \frac{d ^{2}}{d t ^{2}} (y (x, t)) + e^{t}) (t, y (x, t)) + (, (1 \cdot y (x, t) + \frac{d}{d t} (y (x, t)) t)) (4 \frac{d}{d t} (y (x, t)) + e^{t})))

\frac{1}{sin ( x ) - 1} + \frac{1}{1 + sin ( x )}

e^{x} (e^{x} - 2)

- 5^{n} + 7 (- 5^{n - 1})

\frac{d}{d t} ((C) (8000 + 2 x (C, t)))

(5 x^{2} + x + 1) e^{x}

What is (d^2)/(dt^2)((x(t,y(x,t)))(4y(x,t)+e^t)) ?
The answer to (d^2)/(dt^2)((x(t,y(x,t)))(4y(x,t)+e^t)) is