Given that y = 5x^3 + 7x + 3, find dy/dx

This is an example of differentiation. With differentiation the key rule that allows us to differentiate most algebraic functions is "times the coefficient by the power then decrease the power by one". For example, our first term is 5x^3 and this becomes 15x^2 because we multiply 5 (the coefficient) by 3 the (power) and then decrease the power from 3 to 2 . We then look at the next term 7x and it becomes 7 as the power is 1 and the coefficient is 7 so multiplying them both together will give us 7 and when we decrease the power to 0 from 1. Finally, for our last term the power is effectively 0 as there is no x value so any number times 0 is just 0. Therefore, dy/dx = 15x^2 + 7.