anonymous 5 years ago differentiate y=x/square root (x^2+1)

1. anonymous

Use the quotient rule. Do you know what that is?

2. anonymous

yes i just wanted to know the answer because i keep getting something different to the answer given

3. anonymous

so i'm not sure where i went wrong

4. anonymous

What did you get?

5. anonymous

1/(x^2+1)

6. anonymous

I think you forgot -x

7. anonymous

and the correct answer according to the solution is 1/(x^2+1)^(3/2)

8. anonymous

I got $(1/(x^2+1) )-x$

9. anonymous

The derivative is: $-\frac{x^2}{\left(1+x^2\right)^{3/2}}+\frac{1}{\sqrt{1+x^2}}=\frac{1}{\left(1+x^2\right)^{3/2}}$

10. anonymous

robtobey could you show me your working out before reaching what you had come up with in the above post thanks!

11. anonymous

Used Mathematica 8. The request for the derivative from that program was:$D\left[\frac{x}{\sqrt{1+x^2}},x\right]$ Browse over to WolframAlpha.com and enter: derivative of x/square root (x^2+1) Seclect show steps See the attachment

12. anonymous

Product rule: $\dfrac{\mathbb{d}}{\mathbb{d}x}(u\cdot v)=u\cdot \dfrac{\mathbb{d}v}{\mathbb{d}x}+v\cdot \dfrac{\mathbb{d}u}{\mathbb{d}x}$ where u, v are functions of x. The quotient rule is just extra baggage.

13. anonymous

thank you robtobey,romero and INewton!! ^.^

14. anonymous

¬_¬ It was all robtobey.

15. anonymous

but INewton made a lovely conclusion to the question!

16. anonymous

=]