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avai70178
 one year ago
Someone please help.
I understand the chain rule for derivatives but i'm not sure how to use it in this problem.
y=(x^2+1)(x+1)^2
avai70178
 one year ago
Someone please help. I understand the chain rule for derivatives but i'm not sure how to use it in this problem. y=(x^2+1)(x+1)^2

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Loser66
 one year ago
Best ResponseYou've already chosen the best response.1It is not a chain rule, it is product rule. Where are you stuck?

avai70178
 one year ago
Best ResponseYou've already chosen the best response.0I'm not sure if I should use the product rule on both pieces of the equation with the same exponent.

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1Let a = x^2 +1 then a' = ? Let b = (x+1)^2 , then b' =?

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1no, not that a' = 2x, b' is ok.

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1ok, now. y = a*b , then y' = a'b + b'a ok?

avai70178
 one year ago
Best ResponseYou've already chosen the best response.0oops sorry i didnt mean to post that

avai70178
 one year ago
Best ResponseYou've already chosen the best response.0wait well what is a then?

avai70178
 one year ago
Best ResponseYou've already chosen the best response.0if we are using the product rule than a should equal just 2

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1is it not that we defined a = x^2 +1? and b = (x+1)^2??

avai70178
 one year ago
Best ResponseYou've already chosen the best response.0yes and if we take the derivatives of those then we have a'=2 and b'=?

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1I think you got confuse. ok, let me walk you through the concept. Answer me one by one ok? (x) ' =?

avai70178
 one year ago
Best ResponseYou've already chosen the best response.0do you mean derivative of x? cause idk

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1yes, derivative of x =?

avai70178
 one year ago
Best ResponseYou've already chosen the best response.0im sorry i feel dumb

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1ok, I tell you x' =1 \((x^\color{red}{2})' =\color{red}{2}x^1= \color{red}{2}x\) \((x^\color{red}{3})' =\color{red}{3}x^2\) \((x^\color{red}{5})' =\color{red}{5}x^4\) Now, tell me \((x^{10})' =?\)

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1Good, that is called "nrule" , ok?

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1One more thing you should know, derivative of a constant =0, that is (3)' =0 5' =0 10'=0 tell me (234)' =?

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1good!! Now, combine them \((x +y) ' = x' +y' \) \((x^2 +5)' = (x^2)' +5' =???\)

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1now, product rule: (x*y)' = x'*y + y' *x ok?

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1Now, Your problem : \(((x^2+1) *(x+1)^2)' \)

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1apply product rule, right? what do you get?
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