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Math Help - Chain Rule Derivative

  1. #1
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    Talking Chain Rule Derivative

    Find the Derivative using the Chain Rule:

    x^3(2x-5)^4
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  2. #2
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    Quote Originally Posted by Luckyjoshua View Post
    Find the Derivative using the Chain Rule:

    x^3(2x-5)^4
    You also need to use product rule.
    The two functions here are,
    x^3
    (2x-4)^4

    The respective derivatives are:
    3x^2----> Power rule
    2*4(2x-4)^3=8(2x-4)^3---->Chain Rule

    Now apply the product rule,
    u'v+uv'
    We have,
    [3x^2][(2x-4)^4]+[x^3][8(2x-4)^3]
    Thus,
    3x^2(2x-4)^4+8x^3(2x-4)^3
    Factor,
    x^2(2x-4)^3[3(2x-4)+8x(2x-4)]
    Open,
    x^2(2x-4)^3[6x-4+16x^2-32x]
    Thus,
    x^2(2x-4)^3[16x^2-26x-4]
    Factor,
    2x^2(2x-4)^3(8x^2-13x-2)
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