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

The derivative of y with respect to x is:

y' = 54x^17 + 1/x

Note: We used the power rule for differentiation on the first term and the derivative of ln(x) = 1/x for the second term.

Alternatively, we could rewrite the function as:

y = 3x^18 + ln(x) y = 3x^18 + x^(-1)

Then, taking the derivative using the sum rule and power rule, we get:

y' = 54x^17 - x^(-2)