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.

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