1. ## Simplifying a Derivative

I found the derivative using the chain rule, but how do I simplify it? Here it is:

I believe I'm supposed to factor out common factors, but I just don't know where to start.

Thanks.

2. Originally Posted by ttreat31
I found the derivative using the chain rule, but how do I simplify it? Here it is:

I believe I'm supposed to factor out common factors, but I just don't know where to start.

Thanks.
$\displaystyle y' = -9x^2(5x-2)^3(2-x^3)^2 + 15(2-x^3)^3(5x-2)^2$

common factors look like $\displaystyle 3(5x-2)^2(2-x^3)^2$ ... pull'em out.

3. Ah, now I understand. Then would this be the correct answer?

$\displaystyle y'=3(5x-2)^2(2-x^3)^2[-3x^2(5x-2)+5(2-x^3)]$

Edit: According to my homework, this is not simplified fully!?

4. Originally Posted by ttreat31
Ah, now I understand. Then would this be the correct answer?

$\displaystyle y'=3(5x-2)^2(2-x^3)^2[-3x^2(5x-2)+5(2-x^3)]$

Edit: According to my homework, this is not simplified fully!?
the last factor ...

$\displaystyle [-3x^2(5x-2)+5(2-x^3)]$

... can be simplified further.

distribute and combine like terms.

5. Awesome, thank you so much!