Question

How do you use the definition of a derivative to find the derivative of `f(x)=6`?

Answer 1

The definition of derivative is:

`lim_(hrarr0)(f(x+h)-f(x))/h=f'(x)`.

So:

`lim_(hrarr0)(6-6)/h=0`.

Answer 2

The definition of derivative tells you that:
`f'(x)=lim_(Deltax->0)[f(x+Deltax)-f(x)]/(Deltax)` where `Deltax` is an increment of `x` corresponding to an increment of your function `f(x+Deltax)`.
Your function is a constant so you have that:
`f(x)=6`
`f(x+Deltax)=6`
i.e. your function has always the same value, `6`;
You can now write:
`f'(x)=lim_(Deltax->0)[f(x+Deltax)-f(x)]/(Deltax)=`
`f'(x)=lim_(Deltax->0)[6-6]/(Deltax)=0`

hope it helps