Derivative of y = 3x^18 + ln(x) - Step-by-Step Explanation

There are a few different methods you could use to find the derivative of this function, but one common approach is to use the power rule for differentiation and the chain rule for differentiation. Here's one possible way to do it:

y = 3x^18 + ln(x)

To take the derivative of this function, we'll need to use the power rule for differentiation to find the derivative of the first term and the chain rule for differentiation to find the derivative of the second term.

dy/dx = d/dx (3x^18) + d/dx (ln(x))

First, let's find the derivative of the first term using the power rule:

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

Now, let's find the derivative of the second term using the chain rule. Remember that the derivative of ln(x) is 1/x, so we need to multiply by the derivative of the inside function, which is just 1:

d/dx (ln(x)) = 1/x * d/dx (x) = 1/x

Putting it all together, we get:

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

So the derivative of y = 3x^18 + ln(x) is dy/dx = 54x^17 + 1/x.