What is the derivative of #x#?

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Answer 1 · 2014-10-01T17:16:56

We can use the difference quotient or the power rule.

Lets use the Power Rule first.

#f(x) = x=x^1#

#f'(x)=1x^(1-1)=1x^0=1*1=1#

Difference quotient

#lim_(h->0)=(f(x+h)-f(x))/h=(x+h-x)/h=h/h=1#

Also note that #f(x)=x# is a linear equation, #y=1x+b#. The slope of this line is also 1.