## Thomas' Calculus 13th Edition

$g_r=cosθ+sinθ$ $g_θ=-rsinθ+rcosθ$
Take the first partial derivatives of the given function. When taking partial derivative with respect to r, treat $θ$ as a constant, and vice versa: $g_r=(1)cosθ+(1)sinθ=cosθ+sinθ$ $g_θ=-rsinθ+rcosθ$