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

Question

anonymous · Answer

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

anonymous · Answer

yes!

anonymous · Answer

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.

anonymous · Answer

thanks so much, i'm lost in it

anonymous · Answer

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

anonymous · Answer

ok

anonymous · Answer

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:
$$(-10x-5)(5+x-x^2)^4$$

anonymous · Answer

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

anonymous · Answer

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 :)