y = 4(x^3) + 7x ... Find dy/dx

This is a simple differentiation question. To start, you need to know the general method of differentiation. This is:
if y = Axb then dy/dx = (A*b)x^b-1
There are two terms to differentiate in this problem, in the first term, you bring down the 3 and multiply it with 4 to get 12. Then reduce the power by one according to the equation. By executing the same method with the second term, you multiply 7 by 1 since the power of x is 1. Then, you once again reduce the power by 1, which causes it to become x⁰ which is equal to 1. You are therefore left with 7.
Therefore the answer is dy/dx = 12x² + 7