How do you find the derivative of the function $f (x) = m x + b$ $f(x)=mx+b$ ?

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Answer 1 · 2016-10-19T11:22:34

using the definition of differentiation we have $f'(x)=m$

The definition of the derivative is:

$f'(x)=Lim_(hrarr0)(f(x+h)-f(x))/h$

$f'(x)=Lim_(hrarr0)(m(x+h)+b-(mx+b))/h$

$f'(x)==Lim_(hrarr0)(mx+mh+b-mx-b)/h$

$f'(x)==Lim_(hrarr0)(cancel(mx)+mh+cancel(b)-cancel(mx)-cancel(b))/h$

$f'(x)==Lim_(hrarr0)(mcancel(h))/cancel(h)$

$f'(x)==Lim_(hrarr0)(m)$

$:.f'(x)=m$

How do you find the derivative of the function f(x)=mx+bf(x)=mx+bf(x)=mx+b?