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Mathematics 74 Online
OpenStudy (anonymous):

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

OpenStudy (anonymous):

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

OpenStudy (anonymous):

yes!

OpenStudy (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.

OpenStudy (anonymous):

thanks so much, i'm lost in it

OpenStudy (anonymous):

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

OpenStudy (anonymous):

ok

OpenStudy (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: \[(-10x-5)(5+x-x^2)^4\]

OpenStudy (anonymous):

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

OpenStudy (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 :)

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