# Derivative question

1. Feb 5, 2009

### pooker

Our teacher wants us to find derivatives the long way

f(x+h) - (fx) / h

So anyways, on one of my questions 3 / x + 2 , x=8

I know how to find the derivative of 3 / x+2 , but why was their an x=8 next to it? Am I supposed to plug this in after finding the derivative?

2. Feb 5, 2009

### mathstudent88

yes, you need to plug it in for x after you find the derivative.

3. Feb 5, 2009

### HallsofIvy

Staff Emeritus
I disagree with mathstudent88. The basic definition of 'derivative' is 'derivative at a given point'. From what you say, I imagine your teacher is expecting you to put it directly into the definition of the derivative of f at x0:
$$\lim_{h\rightarrow 0} \frac{f(x_0+ h)- f(x_0)}{h}$$
which, for f(x)= 3/(x+2), at x0= 8 is
$$\lim_{h\rightarrow 0}\frac{3/((8+h)+2)- 3/(8+2)}{h}$$
$$= \lim_{h\rightarrow 0}\frac{3/(10+h)- 3/10}{h}$$

Last edited: Feb 5, 2009
4. Feb 5, 2009

### Office_Shredder

Staff Emeritus
With the obvious substitution of x=8 instead of x=2

5. Feb 5, 2009

### HallsofIvy

Staff Emeritus
Thanks, OfficeShredder, I've edited that mistake. (So, now I can pretend I never made it!)