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Math Help - Partial Differentiation and the chain rule, 3 variable

  1. #1
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    Question Partial Differentiation and the chain rule, 3 variable

    Hi,
    I cant seem to get the answers they have got... Its weird how they ask for the partial derivatives when its possible to find the complete derivative (i think lol... im probably wrong though) if you just want to find the partial derivative... how do you know which part to find?

    Also, i put the numerical conditions in after finding the derivative.. is this correct or do you put them in at the beginning?

    The solutions are 85, 178 and 54 respectively.

    Thanks.
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  2. #2
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    gah!

    forgot to attach the file with the question on it
    Attached Thumbnails Attached Thumbnails Partial Differentiation and the chain rule, 3 variable-chain-rule.jpg  
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  3. #3
    Behold, the power of SARDINES!
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    No you don't put the values in until after you take the derivative


    \frac{\partial z}{\partial u}=\frac{\partial z}{\partial x}\frac{\partial x}{\partial u}+\frac{\partial z}{\partial y} \frac{\partial y}{\partial u} =(2x+y^3)(v^2)+(3xy^2)(1)

    x=2(1)^2+0^3=2
    y=2+1e^{0}=3

    Finally pluggin in the values we get

    z_u=(2[2]+3^3)(1^2)+(3[2][3]^2)(1)=31+54=85

    So the first is correct. I didn't check the others, but it seems you are on the right track.

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  4. #4
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    ahh ok, thanks for that.

    im still a little confused with it asking for the partial derivatives though... if you add the product of those partial derivatives.. wouldn't that solution define the full derivative?
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