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Math Help - differentiate absolute value at given point

  1. #1
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    differentiate absolute value at given point

    f: R2-->R is defined by f(x) = absolute value of x. Find Df(1,0).

    So Df(x)=[x/sqrt.(x^2), 0]
    So Df(1,0)= 1/sqrt.1^2=1

    Did I do this right?
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  2. #2
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    Quote Originally Posted by Taurus3 View Post
    f: R2-->R is defined by f(x) = absolute value of x. Find Df(1,0).
    Do you mean f(x,y)= |x|? Or f(x,y)= \sqrt{x^2+ y^2}?

    So Df(x)=[x/sqrt.(x^2), 0]
    So Df(1,0)= 1/sqrt.1^2=1

    Did I do this right?
    If you meant f(x, y)= |x|, for x positive |x|= x so the derivative with respect to x is 1 and the derivative with respect to y is 0. \nabla f(1, 0)= <1, 0>.

    If you meant f(x,y)= \sqrt{x^2+ y^2}, then \nabla f= \left<\frac{x}{\sqrt{x^2+ y^2}}, \frac{y}{\sqrt{x^2+ y^2}}\right> so \nabla f(1, 0)= <1, 0>.
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