Use logarithmic differentiation

Question

Find derivative and of f(x)=(3x^2-4x)^3(x-1)^10/(5x+6) at x=2

Answer 1

Let y = f(x) = (3x²-4x)³(x-1)¹⁰ / (5x+6)

lny = 3ln(3x² - 4x) + 10ln(x - 1) - ln(5x + 6)

y'/y = (18x - 12) / (3x² - 4x) + 10/(x - 1) - 5 / (5x + 6)

y' = y[(18x - 12) / (3x² - 4x) + 10/(x - 1) - 5 / (5x + 6)]

So, when x = 2, we have y' = 4[24/4 + 10 - 5/16] = 4(16- 5/16) = 64- 5/4 = 62.75