Derivative of x^2√(9-x^2) using chain rule | Calculus problem solved

[OtherDguy]

Ok, so I just 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)

 

[Hurkyl]

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)

 

[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)

 

[d_leet]

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)

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

 

[OtherDguy]

Err, product rule rather, sorry.

 

[Hurkyl]

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))

 

[OtherDguy]

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