Question

Derivative calculator of y = x ln x - x.

A) y' = ln x
B) y' = x ln x - 1
C) y' = x + ln x
D) y' = 1 - ln x

Answer 1

The derivative of the function y = x ln x - x is found using the product rule for x ln x and the power rule for -x. The derivative simplifies to *ln x*, resulting in the correct answer A) y' = ln x.

Step-by-step explanation:

The question involves finding the derivative of the function y = x ln x - x. To differentiate this function, we use the product rule for the first term (x ln x) and the power rule for the second term (-x). The product rule states that the derivative of a product of two functions is the first function times the derivative of the second function plus the second function times the derivative of the first function.

For the term x ln x, we treat x as the first function and ln x as the second function giving us 1*ln x + x*(1/x). Simplifying this, we get ln x + 1, and for the term -x, the derivative is simply -1. Combining these results gives us y' = ln x + 1 - 1, which simplifies to y' = ln x. Therefore, the correct answer is A) y' = ln x.