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Math Help - Complex Chain Rule Problem

  1. #1
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    Complex Chain Rule Problem

    Hello All,

    Would someone mind helping me check my work? My answer is very close to the answer given in the back of the book, but isn't exactly the same.

    y=3x^2+\sqrt{2}

    z=\sqrt{1+y}

    v=\frac{1}{\sqrt{3}+4z} find \frac{dv}{dx}

    \frac{dy}{dx}= 3x

    \frac{dz}{dy}= \frac{1}{2\sqrt{1+y}}

    \frac{dv}{dz}= \frac{-4}{(\sqrt{3}+4z)^2}


    \frac{dy}{dx}*\frac{dz}{dy}*\frac{dv}{dz}=\frac{dv  }{dx}

    3x * \frac{1}{2\sqrt{1+y}} * \frac{-4}{(\sqrt{3}+4z)^2}


    3x * \frac{1}{2\sqrt{1+(3x^2+\sqrt{2})}} * \frac{-4}{(\sqrt{3}+4\sqrt{1+3x^2+\sqrt{2})^2}}

    Here is the messy answer I ended up with. The answer in the back of the book matches this exactly EXCEPT it is missing the "2" in the beginning of the denominator...any thoughts?

    \frac{-12x}{2\sqrt{1+3x^2+\sqrt{2}}(\sqrt{3}+4\sqrt{1+3x^  2+\sqrt{2}})^2}
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  2. #2
    Senior Member
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    mistake is, must be
    dy/dx=6x
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  3. #3
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    Thank You!
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