ա) f(x) = (2x – 1)/(1 – x)
f’(x) = ((2x – 1)’(1 – x) – (1 – x)’(2x – 1))/(1 – x)2 = (2 – 2x + 2x – 1)/(1 – x)2 = 1/(1 – x)2
բ) f(x) = (2x2 – 4)/(x + 1)
f’(x) = ((2x2 – 4)’(x + 1) – (x + 1)’(2x2 – 4))/(x + 1)2 = (4x2 + 4x – 2x2 + 4)/(x + 1)2 = (2x2 + 4x + 4)/(x + 1)2
գ) f(x) = (3 – 4x)/x2
f’(x) = ((3 – 4x)’x2 – (x2)’(3 – 4x))/x4 = (-4x2 – 6x + 8x2)/x4 = (4x – 6)/x3
դ) f(x) = (x2 + 1)/(√x)
f’(x) = ((x2 + 1)’√x – √x’(x2 + 1))/(√x2) = (2x1.5 – 0.5x1.5 – 0.5x-0.5)/x = (1.5x1.5 – 0.5x-0.5)/x = (3x2 – 1)/(2x√x)
ա) f(x) = (x4 -x)/x2
f’(x) = ((x4 -x)’x2 – (x2)’(x4 -x))/x4 = (4x5 – x2 – 2x5 + 2x2)/x4 = (2x3 + 1)/x2
ա) f(x) = (5 – 2x6)/(1 – x3)
f’(x) = ((5 – 2x6)’(1 – x3) – (1 – x3)’(5 – 2x6))/(1 – x3)2 = (-12x5 + 12x8 + 15x2 – 6x8)/(1 – x3)2 = (6x8 – 12x5 + 15x2)/(1 – x3)2
գ) f(x) = (√x + 1)/(x3)
f’(x) = ((√x + 1)’(x3) – (x3)’(√x + 1))/((x3)2) = (0.5x2.5 – 3x2.5 – 3x2)/(x6) = (-5x2.5 – 6x2)/(2x6) = (-5√x – 6)/(2x4)
դ) f(x) = (x3 – 1)/(x2 – 1)
f’(x) = ((x3 – 1)’(x2 – 1) – (x2 – 1)’(x3 – 1))/((x2 – 1)2) = (3x4 – 3x2 – 2x4 + 2x)/((x2 – 1)2) = (x4 – 3x2 + 2x)/((x2 – 1)2)
f(x) = (3 – x)/(2 + x)
f’(x) = ((3 – x)’(2 + x) – (2 + x)’(3 – x))/(2 + x)2) = (-2 – x2 – 3 + x2 )/((2 + x)2) = -5/((2 + x)2)
ա) f'(0) = -5/4
բ) f'(-3) = -5
f(x) = (x2 – x)/(x + 1)
f’(x) = ((x2 – x)’(x + 1) – (x + 1)’(x2 – x))/(x + 1)2) = (2x2 + 2x – x – 1 – x2 + x)/((x + 1)2) = (x2 + 2x – 1)/((x + 1)2)
ա) f'(-2) = -1
բ) f'(1) = 1/2
Դավիթ Ապիտոնյան 