Question

Find the derivative:

Answer 1

Hooray!! I have found it.. :P

Answer 2

\[\sqrt[4]{9-x^2}\]

Answer 3

Hahaha! Wait!

Answer 4

Thank God you're here. lol

Answer 5

You need to apply Chain Rule here.. :)

Answer 6

you must know this:

\[\huge \sqrt[n]{a} = (a)^\frac{1}{n}\]

Answer 7

Step by step please. Haha

Answer 8

Yes, I'm familiar. :)

Answer 9

so, (9-x^2)^1/4 right?

Answer 10

So, please write your expression in this form first.. :)

Answer 11

I'm stuck there. Haha

Answer 12

\[(9-x^2)^{\frac{ 1 }{ 4}}\]

Answer 13

You must now know that :

\[\large \frac{d}{dx}(f(x)^m) = m \cdot (f(x)^{m-1}). f'(x)\]

Answer 14

Just try to implement it here...

Answer 15

oh yeeeah... wait, is it now:\[\frac{ 1 }{ 4}(9-x^2)^{\frac{ -3 }{ 4}}\]

Answer 16

Have you forgot anything?? Yes, upto here you are right but it is still incomplete.. :P

Answer 17

How 'bout this? : \[\frac{ 1 }{ 4}(9-x^2)^{\frac{ -3 }{ 4}}(-2x)\]

Answer 18

You are getting it right.. :P

Answer 19

Good... :)

Answer 20

Is that correct? Haha, so what now? I just simplify?

Answer 21

Yes you can simplify it..

Answer 22

2 and 4 you can simplify..

You can again use :

\[\large (a)^{\frac{-1}{n}} = \frac{1}{\sqrt[n]{a}}\]

Answer 23

I got it! Haha. Thaaanks again!

Answer 24

Hey, I have a question. Is there a name for that rule? The one I best response-d.

Answer 25

Which rule??

Answer 26

Oh, sh... I thought I'd only be best-ing one response. lol. The one with where you have to multiply it by f'(x)

Answer 27

Chain rule I said already... :)

Answer 28

I only know the part to bring down the coefficient. Oh, ok ok thanks. I'll look into the chain rule again, must've missed it in the lectures. Thanks!

Answer 29

Actually, from very first problem you are using that rule but you did not know that you were using that rule, Can I show you that??

Answer 30

Ok, sure. I know that there's a chain rule, but I thought it was just to cancel this and that.

Answer 31

Okay tell me what is the derivative of \(e^x\) with respect to x ??

Answer 32

\[xe^\] ?

Answer 33

\[xe^{x-1}\]

Answer 34

You have told this to me, I tolerated it, don't go outside and tell everybody that derivative of \(e^x\) is what you have just told, people will make fun of you.. :P

Answer 35

So, as you are just studying these things so I want to tell you that:

\[\frac{d}{dx} (e^x) = e^x\]

Answer 36

If I have to tell you about these things, it will take time surely..

Answer 37

Oh, oh sorry. Wait, I'll just study first my lectures. Thanks again for your help!