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Differentiation - Chain Rule watch

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    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
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    (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?
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    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
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    (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 + x^2)^5)^4 then that should get you:

    4 \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
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    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
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    (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
    You're out by a factor of 2 - can you see the line I bolded? You should be getting 4 \times 5 \times 2x = 40x \neq 20x
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    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 \times 5 \times 2x = 40x \neq 20x
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    (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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