A path r(t) = (x(t), y(t)) follows the gradient of a function (x, y) if the tangent

A path r(t) = (x(t), y(t)) follows the gradient of a function ƒ(x, y) if the tangent vector r'(t) points in the direction of ∇ƒ for all t. In other words, r'(t) = k(t)∇ƒ_r(t) for some positive function k(t). In this case, r(t) crosses each level curve of ƒ(x, y) at a right angle.

Show that if the path r(t) = (x(t), y(t)) follows the gradient of ƒ(x, y), then

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(1), A F = x' (t) fx