F(x)=(7x^5-3x^3+1)(4x^2-5sqrt(x))

differentiate this but do not use algebra before differentiation, do not factor first.

Use the product rule:

d/dx f(x) * g(x) = f'(x)*g(x)+g'(x)*f(x)

d/dx (7x^5-3x^3+1) = 35x^4-9x^2

d/dx 4x^2-5sqrt(x) = 8x - 5/2 * 1/sqrt(2)

d/dx f(x) = (35x^4-9x^2) * (4x^2-5sqrt(x)) + (8x - 5/2 * 1/sqrt(2)) * (7x^5-3x^2+1)

Hint: use the product rule