Question

let f(x) = 7/(x-9)
According to the definition of derivative f'(x)= lim(t->x) _____________

The expression inside the limit simplifies to a simple fractions with numerator_____ and denominator______
we can cancel the factor _____ appearing in the denominator against a similar factor appearing in the numerator leaving a simple fraction with numerator_________ and denominator ________

taking the limit of this fractional expression gives us f'(x)= ___________

Answer 1

So, show whatever work you have for the first blank.

Answer 2

You still there?

Answer 3

Everything I input it says is wrong so I must not be doing it right

Answer 4

Did you try anything like [7/(t-9) - 7/(x-9)] / (t-x) as t ->x ?

Answer 5

That gives [(7x-63-7t+63)/([t-9][x-9])] / (t-x)

Answer 6

Then, -1/[(t-9)(x-9)]. As t->x, then you get -1/(x-9)^2

Answer 7

Ill give that a shot thank you

Answer 8

Wait!

Answer 9

One mistake. Then, -7/[(t-9)(x-9)]. As t->x, then you get -7/(x-9)^2 There, that's better.

Answer 10

how do you get from your original equation to (-7)/(t-9)(x-9)? sorry to bother again

Answer 11

Go from post 4 directly to my post 7.

Answer 12

what did you do to simplify it from post 4 to post 7