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

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Answer 1 · 2016-12-28T13:48:59

definition of derivative

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

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

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

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

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

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

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