Объяснение:
f'x = (ctg(x^2 × y))' = -1/(sin^2 (x^2 × y)) × (x^2×y)' = -1/(sin^2 (x^2 × y)) × 2 × x × y = - (2×x×y) / (sin^2 (x^2 × y))
f'y = ctg(x^2 × y))' = -1/(sin^2 (x^2 × y)) × (x^2×y)' = -1/(sin^2 (x^2 × y)) × x^2 = -(x^2) / (sin^2 (x^2 × y))
f"xx = ( -(2×x×y) / (sin^2 (x^2 × y)) )' = - (2×x×y)' × 1/ (sin^2 (x^2 × y)) - (2×x×y) × (1/(sin^2 (x^2 × y)))' = - (2×y) / (sin^2 (x^2 × y)) - (2×x×y) × ( -2/(sin^3 (x^2 ×y)) ) × cos(x^2 × y) × 2 × x × y = - (2×y) / (sin^2 (x^2 × y)) + (8×x^2×y^2) × (1/(sin^3 (x^2 ×y)) ) × cos(x^2 × y) = - (2×y) / (sin^2 (x^2 × y)) + ( 8×x^2×y^2 × cos(x^2 × y) ) / (sin^3 (x^2 ×y))
f"yy = (-(x^2) / (sin^2 (x^2 × y)))' = -(x^2) × (-2) × (sin^(-3) (x^2 × y)) × cos (x^2 × y) × x^2 = ( 2 × x^4 × cos (x^2 × y) ) / (sin^3 (x^2 × y))
f"xy = f"yx = - (2×x) / (sin^2 (x^2 × y)) - (2×x×y) / (sin^3 (x^2 × y)) × (-2 × cos(x^2×y) × x^2) = - (2×x) / (sin^2 (x^2 × y)) + 4 (x^3 × y × cos(x^2×y)) / (sin^3 (x^2 × y))
Через три года на счету
[(1,1x - n) * 1,1 + 100 000] * 1,1 = 1,1³x - n * 1,1² + 100 000 * 1,1 =
= 1,1³x - n * 1,1² +110 000
Сумма 1,1³x больше суммы 1,1³x - n * 1,1² + 110 000 на 4950
1,1³x - 11³ x + n * 1,1² - 110 000 = 4950
n * 1,1² = 114 950
n = 95 000
Пётр снял 95 000 рублей