Find the derivative of the function. YOU NEED NOT SIMPLIFY.

Question

y = (3x²e^x) / (9x + 1)

Answer 1

y = (3x²e^x) / (9x + 1)

Using the quotient rule we have:

y' = ((9x + 1)(3x²e^x + 6xe^x) - 9(3x²e^x))/(9x + 1)²

y' = (27x³e^x + 54x²e^x + 3x²e^x + 6xe^x - 27x²e^x)/(9x + 1)²

y' = (27x³e^x + 30x²e^x + 6xe^x)/(9x + 1)²

y' = 3xe^x(9x² + 10x + 2)/(9x + 1)²