Question

Derivative of the sum of natural log of x

A) 1/(x ln(x))
B) ln(x) + 1
C) ln(x)
D) 1/x

Answer 1

The derivative of the natural logarithm of x is 1/x, which is related to the fundamental properties of exponents and logarithms in calculus.

Step-by-step explanation:

The student has asked about the derivative of the natural logarithm of x, which is a topic that involves exponents and logarithmic functions in mathematics. The rule for the derivative of the natural logarithm states that if you have a function f(x) = ln(x), the derivative of that function, denoted as f'(x) or d/dx[ln(x)], is 1/x. This is because logarithms are exponents, and when differentiating ln(x), we apply the laws of exponents and the fundamental properties of logarithms.