## anonymous 5 years ago Find the derivative of the function. g(x) = (5 + 3x)4(5 + x - x2)5

1. anonymous

To clarify, is this the proper equation? $g(x) = (5+3x)^{4}(5+x-x^2)^5$

2. anonymous

yes!

3. anonymous

Alright, I'll get to work. Make sure you're accounting for the product rule, AND the chain rule. This is quite a problem here.

4. anonymous

thanks so much, i'm lost in it

5. anonymous

Start with $(5+3x)^4$ and $(5+x-x^2)^5$ individually. Find their derivatives. You need to use the chain rule.

6. anonymous

ok

7. anonymous

Sorry, doing chemistry stuff at the same time. Your answers should be $12(5+3x)^3$ and $5(5+x-x^2)^4 \times -2x+1$ which simplifies to: $(-10x-5)(5+x-x^2)^4$

8. anonymous

I'm sorry I made a mistake. the second equation's derivative is $(-10x+5)(5+x-x^2)^4$

9. anonymous

Using the product rule (h x j)' = h'j + hj' g' = $g' = [12(5+3x)^3 \times (5+x-x^2)^5] + [(5+3x)^4 \times (-10x+5)(5+x-x^2)^4]$ I'm sure that you can simplify this further. Have at it, and keep practicing this. Wading through these difficult dx/dy problems is key :)