# Thread: How would i rewrite this problem

1. ## How would i rewrite this problem

Sorry im redoing it accidently submitted the wrong thing

2. Here was my attempt it was actuly a derivative problem but i decided not to post in the calculus section.

$\displaystyle \frac {1}{3} (1-e^{6x})^{\frac{-2}{3}} * (- e^{6x} * 6)$

$\displaystyle = (2 - 2e^{6x}) ^{\frac{-2}{3}} * -e^{6x}$

$\displaystyle = \frac{1}{(2-2e^{6x})^{\frac{2}{3}}} - e^{6x}$

3. Originally Posted by x5pyd3rx
Here was my attempt it was actuly a derivative problem but i decided not to post in the calculus section.

$\displaystyle \frac {1}{3} (1-e^{6x})^{\frac{-2}{3}} * (- e^{6x} * 6)$

$\displaystyle = (2 - 2e^{6x}) ^{\frac{-2}{3}} * -e^{6x}$

$\displaystyle = \frac{1}{(2-2e^{6x})}^{\frac{2}{3}}} - e^{6x}$
You can't distribute the two to the binomial expression because that expression is an infinite sum and the 2 is not raised to the same power.

$\displaystyle \frac{1}{3}(1-e^{6x})^{2/3} \cdot -6e^{6x}$

$\displaystyle = 2e^{6x}(1-e^{6x})^{2/3}$

You cannot simplify that further.

EDIT: If you're planning on finding the derivative use the product rule and the chain rule

4. I'm assuming you are taking the derivative of f(x):

$\displaystyle f(x) = (1 - e^{6x})^{\frac{1}{3}}$

In that case, you made errors in both the second and third steps.

(second step) You can't put the multiple of 2 inside the $\displaystyle (1 - e^{6x})^{-\frac{2}{3}}$ term.

(third step) You should be multiplying by $\displaystyle -e^{6x}$, not subtracting $\displaystyle e^{6x}$.

5. Ahhh ok gotcha.. (no need to change the post btw)

6. Originally Posted by e^(i*pi)
$\displaystyle \frac{1}{3}(1-e^{6x})^{2/3} \cdot -6e^{6x}$

$\displaystyle = 2e^{6x}(1-e^{6x})^{2/3}$
A slight correction:

$\displaystyle \frac{1}{3}(1-e^{6x})^{-2/3} \cdot -6e^{6x}$

$\displaystyle = -2e^{6x}(1-e^{6x})^{-2/3}$

7. Originally Posted by icemanfan
I'm assuming you are taking the derivative of f(x):

$\displaystyle f(x) = (1 - e^{6x})^{\frac{1}{3}}$

In that case, you made errors in both the second and third steps.

(second step) You can't put the multiple of 2 inside the $\displaystyle (1 - e^{6x})^{-\frac{2}{3}}$ term.

(third step) You should be multiplying by $\displaystyle -e^{6x}$, not subtracting $\displaystyle e^{6x}$.
Your right... I did i just wrote it on here wrong. thanks for the help both of you

8. So in that case i can rewrite it as

$\displaystyle = \frac{-2e^{6x}}{(1-e^{6x})^{2/3}}$

9. Originally Posted by x5pyd3rx
So in that case i can rewrite it as

$\displaystyle = \frac{-2e^{6x}}{(1-e^{6x})^{2/3}}$
Correct.