avai70178
  • avai70178
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
Calculus1
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SOLVED
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katieb
  • katieb
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Loser66
  • Loser66
It is not a chain rule, it is product rule. Where are you stuck?
avai70178
  • avai70178
I'm not sure if I should use the product rule on both pieces of the equation with the same exponent.
Loser66
  • Loser66
Let a = x^2 +1 then a' = ? Let b = (x+1)^2 , then b' =?

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More answers

avai70178
  • avai70178
a= 2 b=2x+2
Loser66
  • Loser66
no, not that a' = 2x, b' is ok.
Loser66
  • Loser66
ok, now. y = a*b , then y' = a'b + b'a ok?
avai70178
  • avai70178
oops sorry i didnt mean to post that
avai70178
  • avai70178
wait well what is a then?
avai70178
  • avai70178
if we are using the product rule than a should equal just 2
Loser66
  • Loser66
is it not that we defined a = x^2 +1? and b = (x+1)^2??
avai70178
  • avai70178
yes and if we take the derivatives of those then we have a'=2 and b'=?
Loser66
  • Loser66
I think you got confuse. ok, let me walk you through the concept. Answer me one by one ok? (x) ' =?
avai70178
  • avai70178
do you mean derivative of x? cause idk
Loser66
  • Loser66
yes, derivative of x =?
avai70178
  • avai70178
idk
avai70178
  • avai70178
im sorry i feel dumb
Loser66
  • Loser66
ok, 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 \((x^{10})' =?\)
avai70178
  • avai70178
10x^9
Loser66
  • Loser66
Good, that is called "n-rule" , ok?
avai70178
  • avai70178
ok
Loser66
  • Loser66
One more thing you should know, derivative of a constant =0, that is (3)' =0 5' =0 10'=0 tell me (234)' =?
avai70178
  • avai70178
0
Loser66
  • Loser66
good!! Now, combine them \((x +y) ' = x' +y' \) \((x^2 +5)' = (x^2)' +5' =???\)
avai70178
  • avai70178
2x?
Loser66
  • Loser66
yup
Loser66
  • Loser66
now, product rule: (x*y)' = x'*y + y' *x ok?
avai70178
  • avai70178
yes
Loser66
  • Loser66
Now, Your problem : \(((x^2+1) *(x+1)^2)' \)
Loser66
  • Loser66
apply product rule, right? what do you get?
avai70178
  • avai70178
8x+4
avai70178
  • avai70178
i think

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