if u=f(x,y) where x=rcos(θ) , y=r sin(θ) prove ((∂u/∂x))^2 +((∂u/∂y))^2 =((∂u/∂r))^2 +(1/r)((∂u/∂θ))^2


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Question Number 88015 by M±th+et£s last updated on 07/Apr/20

$i f u = f (x, y) w h e r e x = r c o s (θ), y = r s i n (θ)$ $p r o v e$ ${(\frac{\partial u}{\partial x})}^{2} + {(\frac{\partial u}{\partial y})}^{2} = {(\frac{\partial u}{\partial r})}^{2} + \frac{1}{r} {(\frac{\partial u}{\partial θ})}^{2}$
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