Question

Let f(x)=2/(x-4). Then according to the definition of derivative f'(x)=lim t approach x ,I got answer is -2/((t-4)(x-4)),but The expression inside the limit simplifies to a simple fraction with
numerator and denominator I can't figure out, I put -2is incorrect, can you give me solution?
and denominator

Answer 1

what is your definition of the derivative?

Answer 2

i have not seen one with a \(t\) but is must be
\[\lim_{t\to x}\] of something
what are you taking the limit of?

Answer 3

this is my problem,

Answer 4

i have never seen anything like this
is the definition
\[\lim_{t\to x}\frac{f(t)-f(x)}{t-x}\]?

Answer 5

I don't know

Answer 6

oh damn

Answer 7

\[\frac{f(t)-f(x)}{t-x}=\frac{\frac{2}{t-4}-\frac{2}{x-4}}{t-x}\]
\[=\frac{\frac{2(x-4)-2(t-4)}{(t-4)(x-4)}}{t-x}\]\[=\frac{\frac{2x-8-2t+8}{(t-4)(x-4)}}{t-x}\]
\[=\frac{\frac{2(x-t)}{(t-4)(x-4)}}{t-x}\]\[=\frac{-2}{(t-4)(x-4)}\]

Answer 8

take the limit by replacing \(t\) by \(x\) and get \(-\frac{2}{(x-4)^2}\)

Answer 9

yes

Answer 10

I know it,thank you very much