Let f(x)=7/(x-6). Then according to the definition of derivative:

f'(x) = lim x-t (FILL IN THE BLANK)

Help please!!

Question

Let f(x)=7/(x-6). Then according to the definition of  derivative:

f'(x) = lim x->t (FILL IN THE BLANK)


Help please!!

anonymous · Answer

I know the formula for the limit definition: [f(x+h) - f(x)]/h.  But when I plug it in with the given function, the computer tells me that it's wrong

anonymous · Answer

$$
f'(t) = \lim_{x\to t}\frac{f(x)-f(t)}{x-t}
$$

anonymous · Answer

Ohh you're using that formula. So I just plug in t for x?

anonymous · Answer

well, if you let $x\to t$ then $x$ is a dummy variable so you can't really use as an input for the derivative.

anonymous · Answer

It is was $t\to x$ then you would have $f'(x)$ instead of $f'(t)$

anonymous · Answer

i meant t->x sorry!

anonymous · Answer

The dummy variable of your limit can't be recycled as the input variable for the function.

anonymous · Answer

Normally the dummy variable would be $h$ or $a$ or  $\Delta x$, but not $x$ itself.

anonymous · Answer

Ok. It says I got it right now. Thanks for the help!!