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Having trouble with quotient rule  Calc help please.
(x^2 + 1)^4 / x^4
 one year ago
 one year ago
Having trouble with quotient rule  Calc help please. (x^2 + 1)^4 / x^4
 one year ago
 one year ago

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pottersheepBest ResponseYou've already chosen the best response.0
I have to derive that
 one year ago

pottersheepBest ResponseYou've already chosen the best response.0
The answer is supposed to be [4(x^21)(x^2+1)]/x^5 which is not what I get
 one year ago

pottersheepBest ResponseYou've already chosen the best response.0
sorry the answer is [4(x^21)(x^2+1)^3]/x^5
 one year ago

ZeHanzBest ResponseYou've already chosen the best response.1
First write it in the equation editor to get a better look at it:\[\frac{ (x^2+1)^4 }{ x^4 }=\left( \frac{ x^2+1 }{ x } \right)^4\] Now you can also use the Chain Rule, because we have the 4th power as a second step. The derivative is:\[4\left( \frac{ x^2+1 }{ x } \right)^3 \cdot \frac{ x \cdot 2x  1 \cdot(x^2+1) }{ x^2 }=4\left( \frac{ x^2+1 }{ x } \right)^3 \cdot \frac{ x^2 1}{ x^2 }\]
 one year ago

pottersheepBest ResponseYou've already chosen the best response.0
Can I use chain rule where there is a fraction?
 one year ago

ZeHanzBest ResponseYou've already chosen the best response.1
Although we're done differentiating, we could still simplify:\[\frac{ 4(x^2+1)^3(x^21) }{ x^5 }\]
 one year ago

ZeHanzBest ResponseYou've already chosen the best response.1
@pottersheep: as long as there is a chain, you can (have to) use the Chain Rule! The chain here is: 1. u=(x^2+1)/x 2. y=u^4
 one year ago

pottersheepBest ResponseYou've already chosen the best response.0
Thank you for your explanation
 one year ago

ZeHanzBest ResponseYou've already chosen the best response.1
You could have done it without Chain Rule, if you leave the original function as it was:\[\left( \frac{ (x^2 + 1)^4 }{ x^4 }\right)'=\frac{ x^4 \cdot 4(x^2+1)^3 \cdot 2x(x^2+1)^4 \cdot 4x^3 }{ x^8 }\] (still used Chain Rule  see factor 2x!) This now also has to be simplified (begin with dividing everything by x³):\[\frac{ 8x^2(x^2+1)^34(x^2+1)^4 }{ x^5 }=\]\[\frac{ 4(x^2+1)^3(2x^2(x^2+1)) }{ x^5 }=\frac{ 4(x^2+1)^3(x^21) }{ x^5 }\]So we come to the same answer, eventually. You decide which method is easier!
 one year ago

pottersheepBest ResponseYou've already chosen the best response.0
OHhhhh that's what I did before! I see my mistake now! :)
 one year ago
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