How do you use the definition of a derivative to find the derivative of #f(x)=9x-2#?

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Answer 1 · 2017-05-25T11:27:10

see below

the definition of a derivative

#(dy)/(dx)=Lim_(h rarr0)=(f(x+h)-f(x))/h#

for #f(x)=9x-2#

#(dy)/(dx)=Lim_(h rarr0)=(9(x+h)-2-(9x-2))/h#

#(dy)/(dx)=Lim_(h rarr0)=(cancel(9x)+9hcancel(-2)-cancel(9x)+cancel(2))/h#

#(dy)/(dx)=Lim_(h rarr0)=(9cancel(h))/cancel(h)=#

#:.(dy)/(dx)=9#