Final answer:
To differentiate the function y = x^18, we use the power rule of differentiation, resulting in the derivative dy/dx = 18*x^17.
Step-by-step explanation:
To find the derivative of the function y = x18 using the rules of differentiation, specifically the power rule, we follow a simple process. The power rule states that if y = xn, then the derivative of y with respect to x is n*xn-1. Hence, applying the power rule here, we get:
dy/dx = 18*x17
This result comes from multiplying the exponent by the coefficient (which is 1 in this case, as it is not explicitly written), and then subtracting 1 from the exponent. The derivative of x18 with respect to x is 18*x17, which is the solution to the differentiation problem posed by the student.