Derivative of Log e
2026-02-28 15:50 Diff
https://brightchamps.com/en-us/math/calculus/derivative-of-log-e

We can derive the derivative of log e using proofs.

To show this, we consider that log e is a constant value.

There are several methods we use to prove this, such as:

By Definition of a Constant

Using Fundamental Theorem of Calculus

Using Properties of Logarithms

We will now demonstrate that the differentiation of log e results in 0 using the above-mentioned methods:

By Definition of a Constant The derivative of log e can be proved using the definition of the derivative of a constant, which is zero.

To find the derivative of log e, we consider f(x) = log e.

Its derivative can be expressed as: f'(x) = d/dx (log e) = 0

This is because the derivative of any constant value is 0.

Using Fundamental Theorem of Calculus

To prove the differentiation of log e using the Fundamental Theorem of Calculus, We note that log e = 1, a constant.

Therefore, by the theorem: d/dx (c) = 0 for any constant c.

Hence, the derivative of log e is 0.

Using Properties of Logarithms

We will now prove the derivative of log e using properties of logarithms.

Here, we use the formula: log e = 1 Given that, the derivative of a constant is 0, we have: d/dx (1) = 0.

Thus, the derivative of log e is 0.