1. ## Need help understanding what this question is asking.

The given function is:

f(x) = $\frac{5x}{4x+4}$

It's asking for f'(x) = $\lim_{t \to x}$ and says the answer will involve the variables t and x.

I found the derivative of the function using the Quotient Rule, but I don't understand the part where I need to take the limit which will include the variables t and x. Then it says taking the limit of that fractional expression gives f'(x) = _______. Wouldn't you have already found that in the first part of the question?

2. Originally Posted by ImaCowOK
The given function is:

f(x) = $\frac{5x}{4x+4}$

It's asking for f'(x) = $\lim_{t \to x}$ and says the answer will involve the variables t and x.

I found the derivative of the function using the Quotient Rule, but I don't understand the part where I need to take the limit which will include the variables t and x. Then it says taking the limit of that fractional expression gives f'(x) = _______. Wouldn't you have already found that in the first part of the question?
$\displaystyle f'(x) = \lim_{t \to x} \frac{f(x) - f(t)}{x - t}$ is one of the standard 'differentiation from first principles' formulae.