# Thread: Derivative of function

1. ## Derivative of function- tangent/normal

$y = \frac{3x+4}{x-1}$

a. Determine all values for $x$ for which $\frac{dy}{dx}$ exists.

b. Find an expression for $\frac{dy}{dx}$.

Here are my answers..are they correct?

a. All real numbers not equal to 1

b. $\frac{-5}{(x-1)^2}$

2. Originally Posted by live_laugh_luv27
$y = \frac{3x+4}{x-1}$

a. Determine all values for $x$ for which $\frac{dy}{dx}$ exists.

b. Find an expression for $\frac{dy}{dx}$.

Here are my answers..are they correct?

a. All real numbers not equal to 1

b. $\frac{-5}{(x-1)^2}$

a) Correct.

b) Incorrect. Should actually be $-\frac{7}{(x - 1)^2}$.

3. ok, thanks.

4. 2 additional questions:

1) Find line tangent to the curve at $(8,4)$

2) Find line normal to the curve at $(8,4)$and determine the cooridinates of another point where this line intersects the graph.

Here is what I came up with:

1) $y-4=-\frac{7}{64}(x-8)$

2) $y-4=\frac{64}{7}(x-8)
$

Is this correct? I'm unsure what the second part of the second question is asking. Any help is appreciated.