Final answer:
To find (dy)/(dx), use the product rule for differentiation. The derivative of F(x) is 18x and the derivative of G(x) is 10x - 2. Apply the product rule formula to find (dy)/(dx) = 18x + (9x^(2)-7)*(10x - 2).
Step-by-step explanation:
To find (dy)/(dx), we can use the product rule for differentiation. In this case, the function y is the product of two functions: (9x^(2)-7) and (5x^(2)-2x+8). Using the product rule, we can express (dy)/(dx) as (dF(x))/(dx) + (F(x))*(dG(x))/(dx), where F(x) = (9x^(2)-7) and G(x) = (5x^(2)-2x+8).
To apply the product rule, we need to find the derivatives of F(x) and G(x). The derivative of F(x) is dF(x)/dx = 18x and the derivative of G(x) is dG(x)/dx = 10x - 2.
Now, we can substitute these values into the product rule formula to find (dy)/(dx): (dy)/(dx) = (dF(x))/(dx) + (F(x))*(dG(x))/(dx) = 18x + (9x^(2)-7)*(10x - 2).