f(x)=(5x-7x^3)(2+sqrt(x))

Find the derivative

straight-forward product rule

f(x)=(5x-7x^3)(2+sqrt(x))

f(x)=(5x-7x^3)(2+(x)^(1/2))
f ' (x) = (5x - 7x^3)(1/2)x^(-1/2) + (2 + x^(1/2))(5 - 21x^2)
clean it up as needed