Найти производную: 1. f (x) = -1/3·x³+4x²+2x 2.φ (x) = 4/x²+x∛x 3. g (x) = 4ctgx, g' (-2π/3) 4. h (x) = 3x+4/x-3, h' (4)

Question

Ариана Егорова

Математика

26 марта, 20:23

Найти производную: 1. f (x) = -1/3·x³+4x²+2x 2.φ (x) = 4/x²+x∛x 3. g (x) = 4ctgx, g' (-2π/3) 4. h (x) = 3x+4/x-3, h' (4)

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Максим Макаров · Answer 1

f (x) ' = (2 * (5x + 4) ^ (-1)) ' = 2 * (5x + 4) ' * (5x + 4) ^ (-1) ' = 2 * ((5x) ' + (4) ') * (5x + 4) ^ (-1) ' = 2 * (5 + 0) ' * (-1) * (5x + 4) ^ (-2) = - 10 * (5x + 4) ^ (-2) = - 10 / (5x + 4) ^2.

f (x) ' = ((-4x^3 + 1) ^4 - (2 - x) ^5) ' = ((-4x^3 + 1) ^4) ' - ((2 - x) ^5) ') = ((-4x^3 + 1) ' * (-4x^3 + 1) ^4) ' - (2 - x) ' * ((2 - x) ^5) ') = ((-4x^3) ' + (1) ') * (-4x^3 + 1) ^4) ' - ((2) ' - (x) ') * ((2 - x) ^5) ') = (-4 * 3 * x^2 + 0) * 4 * (-4x^3 + 1) ^3 - (0 - 1) * 5 * (2 - x) ^4 = - 24x^2 * (-4x^3 + 1) ^3 + 5 * (2 - x) ^4.

f (x) ' = (x^ (3 / 2) - 2x^ (-4)) ' = (x^ (3 / 2)) ' - (2x^ (-4)) ' = (3 / 2) * x^ (1 / 2) - 2 * (-4) * x^ (-5) = (3 / 2√x) + (8 / x^5).

f (x) ' = ((5x + 1) ^ (-3)) ' = (5x + 1) ' * ((5x + 1) ^ (-3)) ' = ((5x) ' + (1) ') * ((5x + 1) ^ (-3)) ' = (5 + 0) * (-3) * (5x + 1) ^ (-4) = - 15 * (5x + 1) ^ (-4) = - 15 / (5x + 1) ^4.