calculus

f'(x) = 3(x^2+3x+2)^2(2x+3) The derivative of f(x) is equal to the power rule which states that when taking the derivative of a function of the form f(x) = g(x)^n, where n... Answer If f(x) = (x2+3x+2)3, then f'(x) = 3(x2+3x+2)2(2x+3) The power rule states that if f(x) = g(x)n, then f'(x) = n • g(x)n-1 • g'(x), where g'(x) is the derivative of g(x). In this case, g(x) = x2+3x+2, so the derivative g'(x) = 2x+3. Plugging this into the power rule, we get f'(x) = 3(x2+3x+2)2(2x+3).