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Math Help - Partial derivatives

  1. #1
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    Partial derivatives

    Find the first partial derivatives of f(x,y,z) = z * arctan (y/x) :at the point (1, 1, 5).

    I need serious help . i
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  2. #2
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    Quote Originally Posted by simsima_1 View Post
    Find the first partial derivatives of f(x,y,z) = z * arctan (y/x) :at the point (1, 1, 5).

    I need serious help . i
    So you for first partial in z, you take the derivative as if everything except for z is a variable.

    since:

    f(x,y,z)=z* arctan(\frac{y}{x})

    then if z is the only varible, everything attached to it is just some number so you can view the arctan as a constant, say b.

    so:

    f(x,y,z)=z*b

    and the partial derivative of that in terms of z then is:

    f_z(x,y,z)=b

    we substitute b back in and get:

    f_z(x,y,z)=arctan(\frac{y}{x})

    can you do the rest from there?
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  3. #3
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    One more question.... How would i take the partial derivative of the arctangent while holding one of the variables constant?
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  4. #4
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    you just take the derivative of arctangent like normal and the other "variables" you just consider them to be constants so like:

    what's the derivative of:

    arctangent (2x)

    \frac{d}{dx}(arctan (2x)=\frac{1}{1+(2x)^2}*\frac{d}{dx}(2x)=\frac{2}{  1+4x^2}

    So you can treat the other variables like that 2, they're constants, just that you don't know their value.
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