How do you use the definition of a derivative to find the derivative of #f(x)=8x#?

1 Answer
sjc
Dec 28, 2016

definition of derivative

#(dy)/(dx)=Lim_(hrarr0)(f(x+h)-f(x))/h#

Explanation:

for #" "f(x)=8x#

#(dy)/(dx)=Lim_(hrarr0)((8(x+h)-8x))/h#

#(dy)/(dx)=Lim_(hrarr0)((cancel(8x)+8hcancel(-8x)))/h#

#(dy)/(dx)=Lim_(hrarr0)(8cancel(h))/cancel(h#

#(dy)/(dx)=Lim_(hrarr0)(8)=8#

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