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Chain Rule Question

  1. Aug 9, 2017 #1
    I am having difficulty trying to figure the following .

    What is [tex] \frac{\mathrm{d} }{\mathrm{d} x}f(x,y) [/tex] where x is a function of s and t.

    Here is my calculation [tex] \frac{\mathrm{d} }{\mathrm{d} x}f(x(s,t),y) = \frac{\partial f}{\partial x}\frac{\partial x}{\partial t}+\frac{\partial f}{\partial x}\frac{\partial x}{\partial s} [/tex]

    Does this seem correct?
     
  2. jcsd
  3. Aug 9, 2017 #2

    FactChecker

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    That seems wrong. df/dx is just the change of f per unit change of x. It doesn't matter that x is a function of s and t. Once you figure out what df/dx is and you want to evaluate it at some value of x, then you can worry about x being a function of s and t.

    PS. f is actually a function of both x and y, so it is a partial derivative on the left ∂f/∂x.
     
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