Multivariable Functions

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  1. #1
    Just because ygfperson's Avatar
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    Multivariable Functions

    How do you take the derivative of a multivariable function? How would the chain rule work?

    say, add(x,y) == x+y
    the derivative is 1 + dy/dx
    but what of the chain rule?

  2. #2
    Crazy Fool Perspective's Avatar
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    you'll have to be more specific. are you trying to find a partial derivative? are you looking for dy/dx , dx/dy, ....? taking a derivative of a multivariable function is kind of a general term.

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    Toaster Zach L.'s Avatar
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    Basically, for a function z=f(x,y) of two independent variables, to take the partial derivative of z with respect to either x or y, you hold the other one constant. The symbol isn't a 'd', but 'd' will suffice, so dz/dx=df(x,y)/dx.

    You can generalize to directional derivatives however, where you choose some unit vector (in this case, in 2-space), and take the derivative in that direction (often by using cosines of angles).
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    Registered User rahaydenuk's Avatar
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    Let x = x(t) and y = y(t) be differentiable at t and suppose that z = f(x, y) is differentiable at the point (x(t), y(t)). Then z = f(x(t), y(t)) is differentiable at t and:
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