Question

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

Answer 1

`""(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`