# Derivative of x

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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).