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# Differentiation - Chain Rule

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1. 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
2. (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?
3. 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
4. (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
Well: then that should get you:

5. 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

6. (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

You're out by a factor of 2 - can you see the line I bolded? You should be getting
7. 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
8. (Original post by Troopon)
You are right. Mistyped what I had on my paper scribbles. ha
Seems fine now, I think!

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