# Homework Help: Basic Derivative

1. Feb 6, 2006

### OtherDguy

Ok, so I jsut entered Calculus and I'm currently stuck on a problem (no laughing).

Find the derivative of the algebraic function:

$$x^2\sqrt{9-x^2}$$

I tried using the chain rule, but I get confused when composing because x exists in 2 places when you plug in g(x) back into f`(x)

Last edited by a moderator: Feb 6, 2006
2. Feb 6, 2006

### Hurkyl

Staff Emeritus
The thing to learn is that all of the derivative rules are applied just as you would apply ordinary arithmetic rules.

For example, for the function $f(x) = x^2 \sqrt{9 - x^2}$, how would you go about computing f(1.5)?

The first thing you would probably do is to compute (1.5)², right?

So, the first thing you should do when computing the derivative is to find the derivative of x².

Could you show what you have done on the problem? (preferably what you have done after trying to use my hint)

Last edited: Feb 6, 2006
3. Feb 6, 2006

### OtherDguy

I got a bit further. Derivative $$x^2$$ is $$2x$$. First, I used the quotient rule and set $$f(x)$$ to $$x^2$$ and $$g(x)$$ to $$\sqrt{9 - x^2}$$ then used the chain rule to find the derivative of g(x)

4. Feb 6, 2006

### d_leet

The quotient rule really won't help here since you don't have a quotient, but you do have a product...

5. Feb 6, 2006

### OtherDguy

Err, product rule rather, sorry.

6. Feb 6, 2006

### Hurkyl

Staff Emeritus
Ok, so show us how you tried to do the chain rule, and what the problem is!

(You said something about there being multiple x's, but there is only one x in your g(x))

7. Feb 6, 2006

### OtherDguy

Never mind, got it. Was quite a bit of work. Thanks to you both.

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