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Differentiation - Chain Rule

Could someone pls explain how I can solve these differentiation questions using the chain rule.

1. y = (1+(1+x^2)^5)^4

2. y = (1/(3x^2+1)^1/2)^3
Original post by Abstheman
Could someone pls explain how I can solve these differentiation questions using the chain rule.

1. y = (1+(1+x^2)^5)^4

2. y = (1/(3x^2+1)^1/2)^3


What have you tried so far? :redface:
Reply 2
Well so far I have tried subsitute the inside bracket for u and then differentiate. For the first question I got: 20(1+x^2)^4(1+(1+x^2)^3)^310(1+x^2)^4
But this is wrong, the answers say it is: 40x(1+(1+x^2)^5)^3(1+x^2)^4

For the second question I tried the same thing. I got: -9x/(3x^2+1)^3
The answer: -9x/(3x^2 +1)^5/2
Reply 3
Original post by Abstheman
Well so far I have tried subsitute the inside bracket for u and then differentiate. For the first question I got: 20(1+x^2)^4(1+(1+x^2)^3)^310(1+x^2)^4
But this is wrong, the answers say it is: 40x(1+(1+x^2)^5)^3(1+x^2)^4

For the second question I tried the same thing. I got: -9x/(3x^2+1)^3
The answer: -9x/(3x^2 +1)^5/2


Well: (1+(1+x2)5)4(1 + (1 + x^2)^5)^4 then that should get you:

4×(1+(1+x2)5)×(1+(1+x2))4=4×(5×2x×(1+x2)3)×(1++(1+x2))44 \times (1 + (1 + x^2)^5)' \times (1 + (1+x^2))^4 = 4 \times (5 \times 2x \times (1+x^2)^3) \times (1 + +(1+x^2))^4
(edited 8 years ago)
Reply 4
y= (1 + (1 + x^2)^5)^4

dy/dx = 4(1 + (1 + x^2)^5)^3 * the derivitive of (1 + (1+ x^2)^5)

= 4(1 + (1 + x^2)^5)^3 * 5(1 + (1+ x^2))^4 * the derivitive of 1+(1+x^2)

= 4(1 + (1 + x^2)^5)^3 * 5(1 + (1+ x^2))^4 *2x

=40x (1+(1+x^2)^5)^3 (1+(1+x^2)) ^4

which is the answer given :smile:
(edited 8 years ago)
Reply 5
Original post by Troopon
y= (1 + (1 + x^2)^5)^4

dy/dx = 4(1 + (1 + x^2)^5)^3 * the derivitive of (1 + (1+ x^2)^5)

= 4(1 + (1 + x^2)^5)^3 * 5(1 + (1+ x^2))^4 * the derivitive of 1+(1+x^2)

= 4(1 + (1 + x^2)^5)^3 * 5(1 + (1+ x^2))^4 *2x

=20x (1+(1+x^2)^5)^3 (1+(1+x^2)) ^4

which is the answer given :smile:


You're out by a factor of 2 - can you see the line I bolded? You should be getting 4×5×2x=40x20x4 \times 5 \times 2x = 40x \neq 20x
Reply 6
You are right. Mistyped what I had on my paper scribbles. ha

Original post by Zacken
You're out by a factor of 2 - can you see the line I bolded? You should be getting 4×5×2x=40x20x4 \times 5 \times 2x = 40x \neq 20x
Reply 7
Original post by Troopon
You are right. Mistyped what I had on my paper scribbles. ha


Seems fine now, I think! :smile:

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