# Y = x^6.6^x find y' I used a^x = e^(ln a.x)

1. Apr 24, 2012

### WA_EFY

I have a few questions for a quiz
The question was y = x^6.6^x
find y'
I used
a^x = e^(ln a.x)
therefore obtained my answer:

(7x^5)(e^ln( 6 x ))

2. Apr 24, 2012

### RoshanBBQ

Re: Intergration/Differentation

Are you asking what the derivative of
$$x^{6.6^x}$$
is with respect to x?

3. Apr 24, 2012

### WA_EFY

Re: Intergration/Differentation

i am asking what the derivative of
(x^6) times (6^x)
with respect to x

4. Apr 24, 2012

### RoshanBBQ

Re: Intergration/Differentation

How did you get your answer? It's not right.

5. Apr 24, 2012

### WA_EFY

Re: Intergration/Differentation

i know its not right i got it by using
a^x = e^(ln a.x)
and then simplying my answer

6. Apr 24, 2012

### Staff: Mentor

Re: Intergration/Differentation

Did you use the product rule? It's easier to see where you went wrong if you show what you did.

7. Apr 24, 2012

### WA_EFY

Re: Intergration/Differentation

yes I did

8. Apr 24, 2012

### RoshanBBQ

Re: Intergration/Differentation

Are you saying

$$a^x = e^{xln(a)}$$
?

That's certainly true. So we have determined that isn't the cause of your error. What else did you do?

9. Apr 24, 2012

### WA_EFY

Re: Intergration/Differentation

Yes thats what im saying
i then used the product rule and got
6x5×eln6x + x6×6/6x×eln6x

10. Apr 25, 2012

### sharks

Re: Intergration/Differentation

Use LaTex. It's much clearer to display equations.

11. Apr 25, 2012

### HallsofIvy

Re: Intergration/Differentation

Please don't use "x" as a variable and to indicate multiplication!

12. Apr 25, 2012

### sharks

Re: Intergration/Differentation

You could also make a screenshot or take a clear picture of the problem and attach it to your post. Your current problem formatting is confusing, at best.

13. Apr 25, 2012

### RoshanBBQ

Re: Intergration/Differentation

If I'm going to use the order of operations, taught in elementary school, your answer is

$$6x^5e^{xln(6)}+x^7e^{xln(6)}$$

Is that what you were trying to write? Of course it wasn't. It was probably closer to

$$6x^5e^{xln(6)}+x^6\frac{6}{6x}e^{xln(6)}$$

which would result in your incorrect answer given previously. I am assuming you think

$$\frac{d \left (e^{xln(6)} \right )}{dx} = \frac{6}{6x}e^{xln(6)}$$

That is where you are having your problems. Can you tell me what is the derivative of

$$e^{ax}$$

where a is just a constant?

14. Apr 26, 2012

### WA_EFY

Re: Intergration/Differentation

Im sorry I am only new to this and did not know how to enter the function correctly.
I found what I was doing wrong but thanks for the help :)