Question

What is the derivative of \[y=\ln (2)\]?

Answer 1

Hint: The given question is about finding the derivative of the given function. As we can see in the given function that there is no independent function present in the expression, that is, we only have constant with the natural logarithm function. So, we need not carry out the differentiation here. We know that a constant cannot be differentiated in other words the derivative of a constant term is always zero. Hence, we will have value in the given function.

Complete step by step solution:
According to the given question, we are given a function which we have to differentiate.
Differentiation refers to the process to measure the change in a function, which is usually the dependent variable, with respect to the other variable, which is also called the independent variable.
Suppose, we are given a function, \[f(x)={{x}^{2}}\] and we have to find the differentiation, that is, we have to find the change in the function \[f(x)\] when \[x\] changes, so we have,
\[\Rightarrow f'(x)=2x\]
The given function we have is,
\[y=\ln (2)\]---(1)
We can clearly see in the equation (1), that the function does not have any independent variable in it or in other words, the given function is a constant. We know that, a constant function cannot be differentiated or we can say that the differentiation of a constant is always zero, we have,
Differentiating the equation (1), we get,
\[\Rightarrow \dfrac{dy}{dx}=\dfrac{d}{dx}\left( \ln (2) \right)\]
As per what is stated above, we get the value as,
\[\Rightarrow \dfrac{dy}{dx}=0\]

Therefore, the derivative of the given function is 0.

Note: The question should be read properly. The idea of the independent and the dependent variable should be made clear, that is, if there is a function, \[y={{x}^{2}}\], here \[x\] is the independent variable and \[y\] is the dependent variable. Also, the constant function should be understood clearly, that is, a function without the independent variable.