Are these the correct derivatives for these functions?

use the quotient rule to differentiate the function

k(x)= (e^6x)/(x^3+8)

I have got as far as

k '(x) =(x^3+8)(6e^6x)-(e^6x)(3x^2)/(x^3+8)^2

But im unsure how to take it any further would anyone be able to help us?

Your answer is correct! The only thing you can do is put a factor outside in the numerator.

so would that make it

k'(x)= e^6x(6x^3+48-3x^2)/(x^3+8)^2

Quote:

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Originally Posted by Orlando

so would that make it

k'(x)= e^6x(6x^3+48-3x^2)/(x^3+8)^2

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What Siron meant is this:



You just factor using simple algebra.

You can also find differentiation of in the following link:

differentiate (e^(6x))/(x^3+8) - Wolfram|Alpha