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Math Help - chain rule

  1. #1
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    chain rule

    I need some help to differentiate

    g(x)=(1+4x)^5(3+x-x^2)^8
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  2. #2
    Super Member malaygoel's Avatar
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    Quote Originally Posted by c_323_h
    I need some help to differentiate

    g(x)=(1+4x)^5(3+x-x^2)^8
    Let (1+4x)^5 =f(x)
    and (3+x-x^2)=h(x)
    Differentiation of g(x) = differentiation of f(x)h(x)
    = [diff. of f(x)]*h(x) + [diff. of h(x)]*f(x)
    diff. of f(x) = 5[(1+4x)^4]*4
    diff. of h(x)= 8(3+x-x^2)^7{1-2x}
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  3. #3
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    Hello, c_323_h!

    Differentiate: 1+4x)^5(3+x-x^2)^8" alt="g(x) \:=\1+4x)^5(3+x-x^2)^8" />

    Product Rule: . g'(x)\;=\;(1 + 4x)^5\cdot\frac{d}{dx}(3 + x - x^2)^8 +  (3 + x - x^2)^8\cdot\frac{d}{dx}(1 + 4x)^5

    Chain Rule: . g'(x)\;=\;(1 + 4x)^5\cdot8(3 + x - x^2)^7(1 - 2x) + (3 + x - x^2)^8 \cdot5(1 + 4x)^4\cdot4

    Factor: . g'(x)\;=\;4(1 + 4x)^4(3 + x - x^2)^7 [2(1+4x)(1-2x) + 5(3+x-x^2)]

    Simplify: . g'(x)\;=\;4(1+4x)^4(3+x-x^2)^7(17+9x-21x^2)

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