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

[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 ))

 

[RoshanBBQ]

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

 

[WA_EFY]

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

 

[RoshanBBQ]

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

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

 

[WA_EFY]

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

 

[Mark44]

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

 

[WA_EFY]

yes I did

 

[RoshanBBQ]

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

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?

 

[WA_EFY]

Yes that's what I am saying
i then used the product rule and got
6x⁵×e^ln6x + x⁶×6/6x×e^ln6x

 

[DryRun]

Yes that's what I am saying
i then used the product rule and got
6x⁵×e^ln6x + x⁶×6/6x×e^ln6x

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

 

[HallsofIvy]

Yes that's what I am saying
i then used the product rule and got
6x⁵×e^ln6x + x⁶×6/6x×e^ln6x

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

 

[DryRun]

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.

 

[RoshanBBQ]

Yes that's what I am saying
i then used the product rule and got
6x⁵×e^ln6x + x⁶×6/6x×e^ln6x

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?

 

[WA_EFY]

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 :)