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Multivariable CalculusMediumThe Chain Rule & Implicit Differentiation

The Chain Rule & Implicit Differentiation · Medium problem

Let f(x,y)=x2−y2f(x,y) = x^2 - y^2, and change to polar coordinates x=rcos⁡θx = r\cos\theta, y=rsin⁡θy = r\sin\theta. Use the chain rule to find ∂f∂r\dfrac{\partial f}{\partial r} at r=2r = 2, θ=π6\theta = \dfrac{\pi}{6}.