## anonymous 3 years ago Find dy/dx if y= tan9x/x^2

1. anonymous

All you have to do is derivative tan9x/x². Do you know how to? No?

2. anonymous

I thought I did.. and then I did it wrong on the test. I use the product rule but I didnt follow through correctly.

3. anonymous

Do you know quotient rule?

4. anonymous

Yes, that's what I meant, I tried to do that and I didn't know what to do with the tan9x? I can't use it as a constant or I tried to put it outside like 9tanx and it came out wrong

5. anonymous

Well, actually, to derivative the numeration, you have to use chain rule, you know what it is and how to apply it, right?

6. anonymous

I know what it is just no how to use it here. Would it be 1 times 9?

7. anonymous

For chain rule, we know that $\frac{d}{dx}f(g(x)) = f'(g(x)) \cdot g'(x)$Derivative first function and left second function untouched then derivative second function. Let f(x) be tanx and g(x) be 9x. Do you know what to do next?

8. anonymous

No. I don't

9. anonymous

First, we derivative tan(9x). We only need to derivative tan and left 9x untouched. Is this clear?

10. anonymous

Okay, yes.so then I have that - tan9xtimes 2x

11. anonymous

Thank you for your help but at this point I just can't do this.

12. anonymous

Don't say you can't, you can do it! Just derivative the numerator first. Now, what is derivative of tanx?

13. anonymous

sec^2x

14. anonymous

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