Derivative of x is defined as the differentiation of x. If differentiation of x is with respect to x then the differentiation of x will be one that is dx/dx = 1. This is because the numerator and denominator are same, hence it cancels out. If x is treated as constant with respect to some other variable y, then it its differentiation will be zero.
It is important to note this formula for finding out the differentiation of x:-
Differentiation of x along with constant function, d/dx (kx) = k. dx/dx = k `
Here k is constant value.
This can be more clarified by the following below mentioned examples:-
Question 1: Find the differentiation of the following term involving x with respect to x,
Term is y = 10 + 20 x
Solution: Given y = 10 + 20 x
Now by sum property of differentiation, dy/dx = d (10+20x) / dx
Therefore dy/dx = d (10)/dx + d(20x)/dx
So dy/dx = 0+ 20 (1) (because derivative of constant function is zero)
Hence dy/dx = 20
Question 2: Find the differentiation of the following term involving x with respect to z,
Term is y = 100 - 500 x, here is x any constant value
Solution: Given y = 100 - 500 x
Now dy/ dx = d (100 + 500 x) / dx
By Subtraction property of differentiation, dy/dx = d (100)/ dx + d (500x)/ dx
Therefore, dy/dx = 0 + 0 = 0 (This is because here x is constant value, and we know that,
the derivative of constant function is zero).