Question

why differentiation of x = 1, when it is differentiated with respect to x

Answer 1

\[\frac{ d }{ dx } x = 1\] think of the power rule, \[\frac{ d }{ dx } x^n = nx^{n-1}\] so when we have just x, that implies \[x=x^1\] differentiating \[\frac{ d }{ dx } x^1 = 1(x^{1-1}) = 1x^0 = 1\] since we have the exponent property \[x^0 = 1\] hope that answers it!

Answer 2

Is it not that dx/dx =1?

Answer 3

\[\frac{d}{dx}[f(x)]\]is simply the instantaneous slope of \(f(x)\) at any arbitrary point \(x\).

What is the slope of \(y = x\)?