Derivative of y=3x^18+lnx: Step-by-Step Explanation

There are different ways to approach this problem, but one possible method is to use the power rule and the chain rule of differentiation. Here are the steps:

1. Find the derivative of the first term, 3x^18, using the power rule:

dy/dx = 3*18x^(18-1) = 54x^17

2. Find the derivative of the second term, ln x, using the chain rule:

dy/dx = 1/x

3. Add the two derivatives to get the overall derivative of y:

dy/dx = 54x^17 + 1/x

Therefore, the derivative of y with respect to x is:

dy/dx = 54x^17 + 1/x