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Math Help - Partial Derivative Questions

  1. #1
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    Partial Derivative Questions

    Hi i've attempted a few problems from my textbook which i've understood but i've come across 2 questions which have completly got my confused, and wouldnt mind some assistance .

    1) Prove that if z=2xy+x.f\frac{y}{x} then x\frac{{\delta}z}{{\delta}x}+y\frac{{\delta}z}{{\d  elta}y}=z+2xy

    2)If f=F(x,y) and x=re^\theta, y=re^{-\theta} prove that 2x\frac{{\delta}f}{{\delta}x}=r\frac{{\delta}f}{{\  delta}r}+{{\delta}f}{{\delta}\theta} and that 2y\frac{{\delta}f}{{\delta}y}=r\frac{{\delta}f}{{\  delta}r}-{{\delta}f}{{\delta}\theta}
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  2. #2
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    Quote Originally Posted by Kevlar View Post
    1) Prove that if z=2xy+x.f\frac{y}{x}
    To me, this statement is unclear. What is f?
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  3. #3
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    thats what i was wondering but heres a hard copy of the question :\

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