# Thread: Need help with this derivative?

1. ## Need help with this derivative?

The funciton is 3x/(x^2+4)
I have no idea how to differentiate it. Step by step instructions would really help.

2. ## Re: Need help with this derivative?

Use the Quotient Rule.

3. ## Re: Need help with this derivative?

What's the quotient rule? I know the product rule is f(x)g'(x)+f'(x)g(x)

4. ## Re: Need help with this derivative?

Originally Posted by AFireInside
What's the quotient rule? I know the product rule is f(x)g'(x)+f'(x)g(x)
If you don't know the Quotient Rule, you can use the Product Rule if you rewrite the function as 3x(x^2 + 4)^(-1)

5. ## Re: Need help with this derivative?

But what do i do with the -1 exponent?

6. ## Re: Need help with this derivative?

Originally Posted by AFireInside
But what do i do with the -1 exponent?
You would need to use the chain rule to differentiate (x^2 + 4)^(-1)

7. ## Re: Need help with this derivative?

But then the -1 becomes a -2 and it doesn't really get you anywhere

8. ## Re: Need help with this derivative?

Originally Posted by AFireInside
But then the -1 becomes a -2 and it doesn't really get you anywhere
What's wrong with that?

9. ## Re: Need help with this derivative?

Well using the chain rule (x^2+4)^-1 would become -(x^2+4)^-2 x (x^2+4).
I don't see how that simplifies things.

10. ## Re: Need help with this derivative?

No it doesn't... It's the derivative of the inside times the derivative of the outside.

11. ## Re: Need help with this derivative?

Now I'm lost.

12. ## Re: Need help with this derivative?

The inside is u = x^2 + 4. What is its derivative?

The outside is u^(-1). What is its derivative?

13. ## Re: Need help with this derivative?

Originally Posted by AFireInside
Well using the chain rule (x^2+4)^-1 would become -(x^2+4)^-2 x (x^2+4). I don't see how that simplifies things.
If $\displaystyle y(x) = \frac{{f(x)}}{{g(x)}}$ then $\displaystyle y'(x) = \frac{{f'(x)g(x) - f(x)g'(x)}}{{\left[ {g(x)} \right]^2 }}$.

$\displaystyle f(x)=3x~\&~g(x)=x^2+4$

14. ## Re: Need help with this derivative?

I thought chain rule was nf'(x) x f(x)^n-1
So it should be -1(2x)(x^+4)^-2

15. ## Re: Need help with this derivative?

Correct, despite the typo, it should be -2x(x^2 + 4)^(-2).

So now you can apply the product rule.

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