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

(i): 15x^(2)+7 --- in order to arrive at this answer, we can divide the equation into 3 separate parts: 5x^(3) and 7x and 3. For the first part, you would multiply the first number, 5 by the power, in this case, 3, leaving us with 15. Then, you have to decrease the power by 2, leaving us with 15x^(2).

For the second part, the power is actually 1, so 7x^(1). The same process is used, multiply 7 by 1, leaving us with 7. Decrease the power by 1, leaving us with 0. Anything multiplied to the power of 0, is 1. 7x1=7.