найти производную функцию 1) f (x) = x+3 2) f (x) = x^5-x 3) f (x) = 1/x-x^3 4) f (x) = x^2+sqrt (x)

Question

Ева Воронцова

Математика

10 мая, 00:30

найти производную функцию 1) f (x) = x+3 2) f (x) = x^5-x 3) f (x) = 1/x-x^3 4) f (x) = x^2+sqrt (x)

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Игорь Панов · Answer 1

(x) ' = (4 х + 5) ' = (4 х) ' + (5) ' = 4 * 1 * x^{(1 - 1)} + 0 = 4 * x⁰ = 3 * 1 = 4.

f (x) ' = (5 х - 8) ' = (5 х) ' - (8) ' = 5 * 1 * x^{(1 - 1)} - 0 = 5 * x⁰ = 5 * 1 = 5.

f (x) ' = (4x⁵ - 5x⁴.) ' = (4x⁵) ' - (5x⁴) ' = 4 * 5 * x^{(5 - 1)} - 5 * 4 * x^{(4 - 1)} = 20 * x⁴ - 20 * x³ = 20x⁴ - 20x³ = 20x³ (x - 1).

f (x) ' = (x³ - 7x²) ' = (x³) ' - (7x²) ' = 1 * 3 * x^{(3 - 1)} - 7 * 2 * x^{(2 - 1)} = 3 * x² - 14 * x = 3x² - 14x = x (3x - 14).

f (x) ' = (x * (x - 4)) ' = (x) ' * (x - 4) + x * (x - 4) ' = (x) ' * (x - 4) + x * ((x) ' - (4) ') = 1 * (x - 4) + x * (1 - 0) = x - 4 + x = 2x - 4.

f (x) ' = (3 - 2 х) ' = (3) ' - (2 х) ' = 0 - 2 * 1 * x^{(1 - 1)} = - 2 * x⁰ = - 2 * 1 = - 2.