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

解答

\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})))

求解步骤

\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})))

e x p an d e^{x} (e^{x} - 2)

e x p an d - 5^{n} + 7 (- 5^{n - 1})

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

e x p an d (5 x^{2} + x + 1) e^{x}

e x p an d (D + 6) (5 x - (D - 4) = 0)