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

1 Answer
Nov 22, 2016

Answer:

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

Explanation:

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

for #""y=2x#

#""(dy)/(dx)=Lim_(hrarr0)((2(x+h)-2x)/h)#

#""(dy)/(dx)=Lim_(hrarr0)((cancel(2x)+2hcancel(-2x))/h)#

#""(dy)/(dx)=Lim_(hrarr0)((2cancel(h))/cancel(h))#

#(dy)/(dx)=2#