Question

Найти производную, 10 класс

Answer 1

7) f'(x) = 4(√x +3)³ *(√x +3)' = 4(√x + 3)³ * 1/2√x
f'(x₀) = f'(4) = 4(√4 + 3)³ * 1/2√4 = 4*5³ *1/4 = 5³ = 125
8) f'(x) = 1/2√(9 - 2x) *(9 -2x)' = 1/2√(9 - 2x) * (-2) = -1/√(9 -2x)
f'(x₀) = f'(0) = -1/3
9) f'(x) =( (3x² -3)*(1 +4x⁵) - (x³ -3x)*20x⁴ )/(1 + 4x⁵)² =
=(3x² +12x⁷ -3 -12x⁵ - 20x⁷ +60x⁵)/(1 +4x⁵)² = 
= (- 8x⁷ +48x⁵ + 3x² -3)/(1 +4x⁵)²
f'(x₀) = f'(1) = (-8 +48 +3 -3)/(1 +4)² = 40/25 = 8/5 = 1, 6