What is the derivative of x ln x with respect to x? Group of answer choices 1/x x ln x - 1 1 + ln x x ln x + 1/x

The derivative of the function f(x) = x ln(x) with respect to x can be found using the product rule for differentiation, which states that the derivative of two functions multiplied together is the first function times the derivative of the second function plus the second function times the derivative of the first function.

Let's denote: u(x) = x and v(x) = ln(x)

The derivative of u(x) = x is u'(x) = 1. The derivative of v(x) = ln(x) is v'(x) = 1/x.

Applying the product rule, we get:

f'(x) = u(x)v'(x) + v(x)u'(x) f'(x) = x * (1/x) + ln(x) * 1 f'(x) = 1 + ln(x)

So, the derivative of x ln(x) with respect to x is 1 + ln(x).