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Math Help - differential of (x^2 + y^3)^1/2 at (1,2)

  1. #1
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    differential of (x^2 + y^3)^1/2 at (1,2)

    We just started partial derivatives in vector calculus and now we are being introduced to differentials.

    I need to find the differential of (x^2 + y^3)^1/2 at the point (1,2)

    I know that differential is equal to the sum of both partial derivatives so is the answer

    3y^2 / (2(y^3 + x^2)^(1/2) + x/ (y^3 + x^2)^(1/2)
    Last edited by Frostking; February 1st 2009 at 06:27 PM. Reason: wrong information given
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  2. #2
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    Hello,
    Quote Originally Posted by Frostking View Post
    We just started partial derivatives in vector calculus and now we are being introduced to differentials.

    I need to find the differential of (x^2 + y^3)^1/2 at the point (1,2)

    I know that differential is equal to the sum of both partial derivatives so is the answer

    3y^2 / (2(y^3 + x^2)^(1/2) + x/ (y^3 + x^2)^(1/2)
    Actually, the differential df of a function is :
    df=\frac{\partial f}{\partial x} ~dx+\frac{\partial f}{\partial y} ~dy (maybe you learnt it another way...)

    So df_{(x,y)}=\frac{x}{\sqrt{y^3+x^2}} ~dx+\frac{3y^2}{2 \sqrt{y^3+x^2}} ~dy (as you correctly calculated)

    Now let x=1 and y=2
    Last edited by Moo; February 4th 2009 at 02:05 AM. Reason: forgot dy
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