Odpowiedzi

Najlepsza Odpowiedź!
2009-12-25T13:10:16+01:00
A) f(x)= √3 × x² × ⁵√x
f(x) = √3 × x² × ⁵√x = √3 × x² × x^{1/5} = √3 × x^{11/5}
f'(x) = 11√3/5 × x^{6/5}

b) f(x) = 1/x - 4
f(x) = 1/x - 4 = x^{-1} - 4
f'(x) = - x^{-2} = - 1/x²

c) f(x)= (x - 2)³
f(x) = (x - 2)³ = x³ - 6x² + 12x - 8
f'(x) = 3x² - 12x + 12

d) f(x) = x² - 9/x² + 9
f(x) = x² - 9/x² + 9 = x² - 9x^{-2} + 9
f'(x) = 2x + 18x^{-3} = 2x + 18/x³

e) f(x)= x³ - x/x⁴ + 5x
f(x) = x³ - x/x⁴ + 5x = x³ - 1/x³ + 5x = x³ - x^{-3} + 5x
f'(x) = 3x² + 3x^{-4} + 5 = 3x² + 3/x⁴ + 5