How do you use the limit definition to find the derivative of y=x+4?

1 Answer
Steve M
Dec 4, 2016

dy/dx = 1

Explanation:

The definition of the derivative of y=f(x) is

f'(x)=lim_(h rarr 0) ( f(x+h)-f(x) ) / h

So Let f(x) = x+4 then;

\ \ \ \ \ f(x+h) = (x+h) + 4
:. f(x+h) = x+h + 4

And so the derivative of y=f(x) is given by:

\ \ \ \ \ dy/dx = lim_(h rarr 0) ( (x+h + 4) - (x+4) ) / h
:. dy/dx = lim_(h rarr 0) ( x+h + 4 -x-4 ) / h
:. dy/dx = lim_(h rarr 0) ( h ) / h
:. dy/dx = 1

Related questions
See all questions in Limit Definition of Derivative
Impact of this question
1347 views around the world
You can reuse this answer
Creative Commons License