tentukan turunan f(x)= 3x²+x+5/x²+x-1

Jawaban: (2x^2 - 16x - 6)/(x²+x-1)^2 Konsep Turunan f(x) = ax^n adalah f'(x) = na x^(n-1) Turunan fungsi f(x) = u(x)/v(x) adalah f'(x) = (u'(x) v(x) - u(x) v'(x))/ [v(x)]^2 Penyelesaian: f(x)= (3x²+x+5)/(x²+x-1) Maka u(x) = 3x²+x+5 u'(x) = 6x + 1 + 0 = 6x + 1 v(x) = x²+x-1 v'(x) = 2x + 1 - 0 = 2x + 1 f'(x) = [u'(x) v(x) - u(x) v'(x)]/ [v(x)]^2 = [(6x + 1)(x²+x-1) - (3x²+x+5)(2x + 1)]/(x²+x-1)^2 = [(6x^3 + 6x^2 - 6x + x^2 + x - 1) - (6x^3 + 3x^2 + 2x^2 + x + 10x + 5)] / (x²+x-1)^2 = [(6x^3 + 7x^2 - 5x - 1) - ( 6x^3 + 5x^2 + 11x + 5)] / (x²+x-1)^2 = (2x^2 - 16x - 6)/(x²+x-1)^2 Jadi, turunannya adalah (2x^2 - 16x - 6)/(x²+x-1)^2.