Finding Derivatives: h(2)=4, h'(2)=-3, d/dx(h(x)/x)|x=2

[Joyci116]

Homework Statement

If h(2)=4 and h'(2)=-3, find
\left.\frac{d}{dx}\frac{h(x)}{x}\right|_{x=2}

Homework Equations

n^n-1 (power rule)

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.

 

[ArcanaNoir]

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

 

[SammyS]

Homework Statement

If h(2)=4 and h'(2)=-3, find \displaystyle \left[\frac{d}{dx}\left(\frac{h(x)}{x}\right) \right|_{x=2}

Homework Equations

n^n-1 (power rule)

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.

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

 

[Joyci116]

SO the derivative would be -3/4?

 

[SammyS]

No. Are you using the quotient rule?

Helps to show your work.

 

[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.

 

[SammyS]

(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)}\,?

 

[Mark44]

Um, h(x)=4,

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

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.

Forget the numbers for now.[/color]

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.

 

[Joyci116]

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

 

[Mark44]

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

What's x' ?
Simplify what you have.

Then evaluate everything at x = 2.

 

[Joyci116]

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

 

[Mark44]

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