Question

What is the derivative of $\ln 5$?

Answer 1

For solving this question you should know about the differentiation of logarithmic functions and how to calculate the derivatives. In this question we will differentiate to $\ln 5$ with respect to any variable. But as we know that $\ln 5$ is a constant value and the differentiation of a constant is 0 because it will never change, so the rate of change of the $\ln 5$ function will always be zero.

Complete step by step solution:
According to our question if we see that it is asked of us to determine the derivative of $\ln 5$. So, as we know that the differentiation of any logarithmic function will be $\dfrac{d}{dx}\ln \left( x \right)=\dfrac{1}{x}$, so we can say that the derivative of $\ln x$ is always same as that. If we see examples of the, then:
Example 1: Find the derivative of $\ln \left( 5x \right)$.
We have to find the derivative of $\ln \left( 5x \right)$, so as we know,
$\dfrac{d}{dx}\ln \left( 5x \right)=\dfrac{1}{5x}.5=\dfrac{1}{x}$
But if we see our question then, we know that $\ln 5=1.6094$, which is a constant value. And we know that the differentiation of the constant is always zero. And the derivatives of constants are always zero because they do not change with the variable in whose respect they are going to differentiate. So, the differentiation of $\ln 5$,
$\begin{aligned} & \Rightarrow \dfrac{d}{dx}\ln 5=? \\\ & \Rightarrow \dfrac{d}{dx}\left( 1.6094 \right)=0 \\\ \end{aligned}$

So, the derivative of $\ln 5$ is equal to zero.

Note:
During solving the differentiation of any term we always have to be assured that the term which we are differentiating and the variable with whose respect we differentiate to this, always have the same variable, unless this will be a constant for that and the differentiation will be zero.