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Math Help - partial derivatives of functions wrt to another function?

  1. #1
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    partial derivatives of functions wrt to another function?

    I came across this problem in a text I am using currently and was confused by the notation and am not sure of the answer

    given a function f = h(g_1, g_2, g_3)
    if h=x^2 - yz and f = h(x+y, y^2,x+z) then is it correct to apply the pointwise vector coordinate function and get f = (x+y)^2 -y^2(x+z)

    This seemed like a trivial problem but the notation really confuses me.
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  2. #2
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    Re: partial derivatives of functions wrt to another function?

    Quote Originally Posted by knkumar View Post
    I came across this problem in a text I am using currently and was confused by the notation and am not sure of the answer

    given a function f = h(g_1, g_2, g_3)
    if h=x^2 - yz and f = h(x+y, y^2,x+z) then is it correct to apply the pointwise vector coordinate function and get f = (x+y)^2 -y^2(x+z)

    This seemed like a trivial problem but the notation really confuses me.
    Yes, that exactly what the notation means: f= h(x+ y, y^2, x+ z)= (x+y)^2- (y^2)(x+ z). The fact that x, y, z are used as "place holders" in both functions is irrelevant.
    This is exactly the same as if it were h(u, v, w)= u^2- vw
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