# Finding the Derivative

1. Oct 20, 2011

### Joyci116

1. The problem statement, all variables and given/known data
If h(2)=4 and h'(2)=-3, find
$$\left.\frac{d}{dx}\frac{h(x)}{x}\right|_{x=2}$$

2. Relevant equations
n^n-1 (power rule)

3. The attempt at a solution
I don't know how to get this started. It seems like I am having trouble with derivatives. I can do simple derivatives with the power rule, product rule, and quotient rule, but I do not know what the line on the right means, nor do I understand what the d/dx times the quantity of h(x)/x means.

Last edited by a moderator: Oct 20, 2011
2. Oct 20, 2011

### ArcanaNoir

It means find the derivative of f(x)/x when (or, at the point where) x equals 2.

3. Oct 20, 2011

### SammyS

Staff Emeritus
d/dx times the quantity of h(x)/x means: the derivative of h(x)/x

the line on the right means: evaluate the derivative at x = 2

4. Oct 20, 2011

### Joyci116

SO the derivative would be -3/4?

5. Oct 20, 2011

### SammyS

Staff Emeritus
No. Are you using the quotient rule?

6. Oct 20, 2011

### Joyci116

Um, h(x)=4, because x=2 so h(2)=4; x=2, so I get 1/2. But you don't understand how you would the the quotient rule using that value. There is the product rule if you rearrange the formula to 1(2)^-1
I'm sorry, I'm a little confused.

7. Oct 20, 2011

### SammyS

Staff Emeritus
(Don't put 2 in for x just yet.)

What is the derivative of $\displaystyle \frac{h(x)}{x}$ , using the quotient rule?

If that doesn't make sense, then what is the derivative of $\displaystyle \frac{h(x)}{g(x)}\,?$

8. Oct 20, 2011

### Staff: Mentor

No, you can't say this. You don't know what h(x) is, only what its value is at a particular x value.
Forget the numbers for now.

1. Find the derivative of h(x)/x. I would use the quotient rule.
2. Evaluate the derivative you found in #1 at x = 2.

9. Oct 20, 2011

### Joyci116

$\frac{x[h'(x)]-h(x)x'}{x^{2}}$

10. Oct 20, 2011

### Staff: Mentor

What's x' ?
Simplify what you have.

Then evaluate everything at x = 2.

11. Oct 20, 2011

### Joyci116

x=2
[2(-3)-4(0)]/2^2 =-3/2

12. Oct 20, 2011

### Staff: Mentor

Not quite, but you're close. What's x'? (It's not 0.)