find the derivative of ((x^(2)+1)^(4))/((2x+1)^(3)(3x-1)^(5))

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Try logarithmic differentiation.For example let y = [(x+8)^9] / [(2x-15)^10]Now take "ln" of both sides using the rules of logs:ln y = ln {[(x+8)^9] / [(2x-15)^10]}ln y = ln (x+8)^9  - ln (2x-15)^10ln y = 9ln (x+8) - 10ln (2x-15)Now take derivative of both side:1/y * y' = 9/(x+8) - 10/(2x-15) x 2Now simply solve for y' by multiplying both sides by y.This method works great for messy polynomial functions or even mixture of polynomials and exponential functions.Hope this helps