How do you find the derivative of the function #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#