Question

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

Answer 1

`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`